The measurement and analysis of road vehicle drag forces
252
This item was submitted to Loughborough's Research Repository by the author. Items in Figshare are protected by copyright, with all rights reserved, unless otherwise indicated. The measurement and analysis of road vehicle drag forces The measurement and analysis of road vehicle drag forces PLEASE CITE THE PUBLISHED VERSION PUBLISHER © M.A. Passmore LICENCE CC BY-NC-ND 4.0 REPOSITORY RECORD Passmore, Martin A.. 2010. “The Measurement and Analysis of Road Vehicle Drag Forces”. figshare. https://hdl.handle.net/2134/7038.
Transcript of The measurement and analysis of road vehicle drag forces
This item was submitted to Loughborough's Research Repository by the author. Items in Figshare are protected by copyright, with all rights reserved, unless otherwise indicated.
The measurement and analysis of road vehicle drag forcesThe measurement and analysis of road vehicle drag forces
PLEASE CITE THE PUBLISHED VERSION
PUBLISHER
© M.A. Passmore
LICENCE
CC BY-NC-ND 4.0
REPOSITORY RECORD
Passmore, Martin A.. 2010. “The Measurement and Analysis of Road Vehicle Drag Forces”. figshare.https://hdl.handle.net/2134/7038.
This item was submitted to Loughborough University as a PhD thesis by the author and is made available in the Institutional Repository
(https://dspace.lboro.ac.uk/) under the following Creative Commons Licence conditions.
For the full text of this licence, please go to: http://creativecommons.org/licenses/by-nc-nd/2.5/
' ..
, .. "
-LOUGHBOROUGH __ UNIVERSITY OF TECHNOLOGY
LIBRARY AUTHOR/FILING TITLE
·PASSMca...r M A.. . -------------------------~-------------------
. , --- -- - -- --- ----------------- -- -- --- - ---- - - --.--- -wo.,.-
, ACCESSION/COPY NO.
, 0 '\-00\:>;'$ b ----------------- ---- --- ---- -------- ----- -- --- - - --~ c-" VOL. NO. _ CLASS MARK
-7 JUN '!IllS ·30 JUN1995
14APR _
23 Nav 1997 ·2 MAY ZOIIO 28 JUN 1996
120Ee 1991
- - - - - - ~~ .... _ ..... ". - "
0360000568
IIIIIIIIIIII~IIIIIIIIIIIIIIIIIIIIIIIIIIIIII
.' 'w
". \-:
THE MEASUREMENT AND ANALYSIS OF ROAD VEHICLE DRAG FORCES.
M.A.Passmore
Submitted for the degree of Doctor of Philosophy in the Department of Transpon Technology
Loughborough University, August 1990.
© M A Passmore 1990.
Loughborough University of Technology Library
!)rHe ~ "I, -~'o.ss
~~c (J'-tOIl 00 &'0
--- ------
Instrumented test vehicle at Bruntingthorpe proving ground.
Dedication.
To Sandra.
For her patience and love.
i
Summary
Accurate measurement of a vehicle's resistance to motion on a road (the 'road load'), and the
separation of this resistive force into its contributory components is of fundamental
importance to generate the data required for vehicle performance assessment, the calibration
of a modern chassis dynamometer and for comparing the drag of different vehicles or vehicle
configurations. Established methods of determining road load on a test track are the
coastdown and steady state torque tests, but environmental variability Oargely due to ambient
wind) and differences in the vehicle operating conditions cause wide variation in the results.
This thesis describes a comprehensive study into methods of acquiring and analysing road
load data at a test track. A mathematical model of the vehicle travelling in a straight line, in the
presence of ambient wind, is developed and may be applied to measured data obtained in
both the coastdown and the steady state test modes. The model includes the aerodynamic
drag, tyre losses, transmission and un-driven wheel losses and the variation of aerodynamic
drag with yaw angle. Experimental data obtained at a test track, using advanced
instrumentation (including on-board anemometry and wheel torque meters) are analysed to
obtain estimates of the coefficients in the road load equation.
The results from an initial study demonstrate the importance of measuring the local wind at
the test vehicle and the transmission losses if the total drag is to be accurately measured and
separated into its contributory components. The coastdown method is shown to be more
accurate and repeatable than the steady state method, and is therefore used as the basis of an
advanced test procedure.
Up to four coefficients can be determined from the coastdown data using a parameter
optimisation routine. This routine fits the mathematical model to the measured coastdown
profile to obtain estimates of the road load coefficients including the variation of aerodynamic
drag coefficient with yaw angle. Results using this analytical method show that all four
coefficients can be determined from coastdown data if there is sufficient ambient wind, and
hence lay the basis for an advanced test method using only data from track tests. Constrained
methods, where one or more of the parameters is fixed, can be used to investigate a single
source of drag. The reduction in the total number of tests required to achieve an acceptable
level of accuracy in the variable coefficients when using the constrained method is
demonstrated.
ii
Acknowledgements
This work was conducted at the Department of Transport Technology, Loughborough
University and was fmancially supported by the SERC and the Ford motor company.
The research was supervised by Mr. E.G.Jenkins and Or G.G.Lucas whose guidance and
contribution to the work is much appreciated. Their encouragement to publish results and
. advice in the preperation of this thesis has been invaluable.
Help, encouragement, and support has been given by members of the research staff at the
Department of Transport Technology, particularly my office colleague of some four years
J.Carrotte.
The author would also like to express his appreciation to all the technical staff who have been
involved in the project and in particular to G.Knowles and E.Smith for their technical
assistance in the design and building of the vehicle instrumentation, and to Mr K.Coulthard
for the construction of the mechanical components and for his involvement in the testing.
The author would like to thank the people mentioned above and all the members of staff in
the Department of Transport Technology with whom it has been a pleasure to work.
Finally the author would like to thank his family for their support and encouragement, and
his wife for her proof reading of this thesis, and her patience and understanding throughout
the preperation of this work.
ill
List of contents
Dedication
Summary
Acknowledgements
List of contents
List of Figures
List of Tables
Nomenclature
Chapter 1 : Introduction.
List of contents
Page
i
ii
iii
iv
x
xii
xiv
1.1 Introduction. 2
1.2 Review of track test methods. 5
1.2.1 Coastdown method. 7
1.2.2 Steady state method. 10
1.2.3 European regulations. 11
1.3 Rig measurements of drag components. 12
1.3. 1 Tyre testing. 12
1.3.2 Wind tunnel testing. 13
1.4 Review of chassis dynarnometer calibration methods. 14
1. 5 Accuracy of road load data. 16
1. 6 Objectives of the research programme. 16
1.6.1 Development of a mathematical model. 17
1.6.2 Application of on board anemometers. 17
1.6.3 Application of a simulation program. 17
1.6.4 Comparison of coastdown and steady state torque methods 18
1.6.5 An advanced test system. 18
iv
List of contents
Chapter 2 : Development of the Mathematical Model.
2.1 Introduction to the model
2.2 Mechanical contribution
2.2.1 Tyre rolling resistance
2.2.1.1 Nonnalload
2.2.1.2 Speed
2.2.1.3 Ambient temperature
2.2.1.4 Tyre conditioning
2.2.1.5 Inflation pressure
2.2.1.6 Applied torque
2.2.2 Drive-line losses
2.2.3 Other losses
2.3 Aerodynamic contribution
2.3.1 Basic vehicle aerodynamics
2.3.2 Origin of the aerodynamic forces
2.3.3 Aerodynamic drag
2.3.4 Aerodynamic lift
2.3.5 Aerodynamic side-force
2.3.6 Summary of the aerodynamic effects
2.4 Summary of the model
2.5 A simplified model
Chapter 3 : Vehicle instrumentation and data acquisition.
3.1 Introduction.
3.2 General ArrangemenL
3.3 Engine Torque MeasuremenL
3.3.1 Engine Torque Calibration.
v
21
22
22
23
24
26
26
27
27
27
29
29
30
31
32
36
37
38
39
39
42
43
43
44
List of coments
3.4 Wheel Torque MeasuremenL 44
3.4.1 Wheel Torque Calibration. 45
3.5 Vehicle Speed. 45
3.5.1 Vehicle Speed Calibration. 46
3.6 On-board Anemometry. 46
3.7 Temperature and pressure measuremenL 48
3.8 Data acquisition system. 48
3.8.1 Description of the Hardware. 48
3.8.2 Description of the software. 49
3.9 Summary. 50
Chapter 4 : Wind Tunnel Tests.
4.1 Introduction 52
4.2 MlRA full-scale wind tunnel 52
4.3 Blockage and 'horizontal buoyancy' correction 53
4.4 Vehicle configurations 54
4.5 Wind tunnel results 55
4.5.1 Coefficient of drag 55
4.5.2 Coefficient of lift 56
4.5.3 Coefficient of side force 56
4.6 Validation of the mathematical model 56
4.6.1 Drag effects 56
4.6.2 lift effects 57
4.6.3 Side force effects 58
4.7 Calibration of the on-board anemometers 58
4.7.1 Tests in the Transport Technology open section tunnel 58
4.7.2 Tests in the MlRA tunnel 59
vi
List of contents
4.7.3 Airspeed calibration at the test track
4.7.4 Summary of calibration
Chapter 5: Test programme and analysis of results.
5.1 Test Programme
5.1.1 Environmental conditions
5.1.2 Vehicle preparation
5.1.3 Test procedure
5.2 Summary of analytical techniques
5.3 Coastdown analysis
5.3.1 Integration scheme
5.3.2 Extracting the coefficients
5.3.3 Scaling
5.3.4 Estimating the accuracy of the coefficients
5.3.5 Flexibility in the analysis
5.4 Steady state analysis
5.4.1 Extracting the coefficients
5.4.2 Estimating the accuracy of the coefficients
5.5 Driveline losses
5.5.1 Coastdown
5.5.2 Steady state
5.6 Undriven wheel losses
5.7 Mean coefficients and overall accuracy
Chapter 6 Validation of analytical software.
6.1 Introduction.
6.2 The simulation program.
vii
61
62
64
64
65
65
66
66
67
68
69
69
69
71
71
72
73
73
74
74
75
77
77
List of contents
6.2.1 Equation of motion. 78
6.2.2 Wmd generation 78
6.2.3 Instrument and vehicle dynamics. 79
6.2.4 Superposition of noise. 79
6.2.5 The complete model. 80
6.3 Coefficient sensitivity analysis. 80
6.4 Summary of the simulated data. 82
6.5 Discussion of results from simulated data. 85
6.5.1 Four tenn analysis. 85
6.5.2 Three tenn analysis. 87
6.6 Anemometer calibration errors. 88
Chapter 7 Results and Discussion - Initial study.
7.1 Introduction. 91
7.2 Practical application of coastdown and steady state methods. 91
7.3 Application of on-board anemometers. 91
7.4 Steady state results. 97
7.5 Transmission losses. 100
7.5.1 Coastdown (off-load). 101
7.5.2 Steady state (on-load). 102
7.5.3 Comparison of transmission losses. 103
7.6 Undriven wheel losses. 103
7.7 Summary of initial study. 104
Chapter 8 Results and discussion - An advanced coastdown method.
8.1 Introduction
8.2 Assessment of results using the three tenn analysis
viii
107
108
List of cOnJents
8.3 Constrained analysis.
8.4 Development of a four tenn analysis.
8.5 Driveline losses in coastdown.
8.6 Summary of the results.
Chapter 9 Conclusions and recommendations
9.1 Conclusions
9.1.1 Mathematical model
9.1.2 Application of on-board anemometers
9.1.3 Simulation program
9.1.4 Comparison of coastdown and steady state methods
9.1.5 Advanced drag measurement method
9.2 Recommendations for further work
References
Bibliography
Appendices
Appendix A
Summary of sections ofECE 83/351 regulations penaining to road load
measurement and setting of chassis dynamometer power absorption unit.
(Based on appendices 2, and 3 of the regulation)
Appendix B On-board anemometry specification. (Manufacturers spec.)
Appendix C
Operating instructions for on-board data acquisition system.
Appendix D
Analytical integration of the coastdown curve.
ix
114
117
121
123
125
125
126
127
127
128
129
132
135
138
144
146
159
1---
Listoffigures
List of Figures
1 Coastdown proflies
2 Residuals from fit to real data (polynomial method of differentiation)
3 General relationship between loss modulus temperature and frequency
of a typical tyre compound
4 Rolling resistance against speed
5 Rolling resistance of a radial car tyre as a function of a cavity temperature and speed
6 Effect of temperature on rolling resistance coefficient
7 Effect of applied torque on rolling resistance coefficient
8 Basic air flow pattern around vehicle
9 MIRA wind tunnel force and moment convention
10 Velocity vector diagram
11 Variation of aerodynamic drag with yaw angle for a typical car
12 Calculated AD against wind speed for various wind angles (unconstrained analysis)
13 Calculated BD against wind speed for various wind angles (unconstrained analysis)
14 Calculated CD against wind speed for various wind angles (unconstrained analysis)
15 Yaw angle against vehicle speed (ECE 15.05) regulations worst case)
16 Variation of aerodynamic lift with yaw angle for a typical car
17 Vehicle tyre running at a slip angle
18 B lock diagram of vehicle instrumentation
19 Engine torque calibration
20 Wheel torque transducer schematic
21 Wheel torque meter system layout
22 Wheel torque meter calibration (1)
23 Wheel torque meter calibration (2)
24 Vehicle speed calibration
25 Schematic of on-board anemometers
26 Computer hierarchy
27 On-vehicle software
28 Instrumentation data
29 MIRA wind tunnel installation
30 Test vehicle in MIRA wind tunnel in base form
31 Test vehicle in MIRA wind tunnel with instrumentation
32 Aerodynamic characteristics for base vehicle (Configuration A)
33 Aerodynamic characteristics for instrumented vehicle (Configuration B)
x
List offigures
34 Coefficient of drag against yaw angle. MIRA wind tunnel
35 Coefficient of lift against yaw angle. MIRA wind tunnel
36 Coefficient of side force against yaw angle. MIRA wind tunnel
37 Coefficient of drag against yaw angle squared. MIRA wind tunnel
38 Coefficient of drag. Comparison of measured and modelled data
39 Coefficient of lift against yaw angle squared. MIRA wind tunnel
40 Coefficient of lift. Comparison of measured and modelled data
41 Anemometer airspeed calibration. Transport Technology open
section wind tunnel
42 Anemometer airspeed calibration. MIRA wind tunnel
43 Anemometer calibration with yaw angle. MIRA wind tunnel
44 Anemometer yaw angle calibration. MIRA wind tunnel
45 Simulation block diagram
46 Spatial variation of the wind
47 Variation of RMS curve fitting error with KD
48 Simulated coastdown data (vh = 3 ms·I , Vx = 3 ms· l )
49 Superimposed actual and measured airspeed and yaw angle data
from simulation
50 Data obtained during coastdown. (ambient wind within ECE 15.04 limits)
51 Data obtained during coastdown (high wind condition)
52 Residuals from curve fit to coastdown data. (Low wind conditions)
53 Residuals from curve fit to coastdown data. (High wind conditions)
54 Uncorrected steady state data
55 Corrected steady state data
56 Residuals from steady state curve fit
57 Steady state test data (Runs in opposite directions averaged)
58 Offload driveline drag measured during a single coastdown test
59 Corrected steady state data, showing the driveline losses
60 Onload driveline drag measured during steady state
61 Undriven wheel losses against speed for a single wheel
62 CD ('I') characteristics determined from coastdown data and the wind tunnel
63 Comparison of the yaw dependent component of aerodynamic drag
derived from coastdown and wind tunnel data
64 Contributions to vehicle drag
CIOn-board computer memory arrangement
C2 Subroutine organisation
xi
List of tables
List of Tables
1.1 Vehicle drag measurement methods
4.1 Airspeed calibration data from track test
6.1 Coefficient sensitivities calculated using simulated data
6.2 Sensitivity of the yaw coefficient Ko
6.3 Vehicle parameters
6.4 Ambient wind characteristics
6.5 Anemometer dynamic characteristics
6.6 Imposed noise levels
6.7 Summary of simulation cases
6.8 Results for the four tenn analysis
6.9 Results for three tenn analysis (Ko fixed)
7.1 Wind levels during testing compared with EEC limits
7.2 Coastdown data gathered during low wind conditions
7.3 Coastdown data gathered in high wind conditions
7.4 Effect of neglecting ambient wind correction
7.5 Summary of non-anemometer results reported by Emtage
7.6 Steady state test results
7.7 Steady state results for averaged data
7.8 Driveline losses in coastdown
7.9 Steady state driveline losses
7.10 Undriven wheel losses
7.11 Summary of initial study results
8.1 Example set of six coastdowns
8.2 Driveline losses for the six coastdowns in table 8.1
8.3 Paired coastdown results using three tenn analysis
8.4 Confidence intervals - three tenn analysis
8.5 Population standard derivations calculated using X2
8.6 Confidence internals (%) at the 95% confidence level against number of tests - three
tenn analysis
8.7 Two tenn analysis CD = 0.39
xii
List of tables
8.8 Confidence internals (%) at the 95% confidence level against number of tests - tyre
losses only
8.9 Paired coastdown results using four term analysis
8.10 Confidence intervals (%) at the 95% confidence level against number of tests - four
term analysis
8.11 Four term analysis for windy conditions
8.12 Summary of driveline loss results
8.13 Summary of results for the test vehicle
xiii
Nomenclature
Nomenclature
Units
A Vehicle projected frontal area m2
Aa Constant drag term N
Ao Constant drag coefficient
At Transmission losses constant Coefficient
A" Constant undriven wheel drag N
b Order of rolling loss speed dependence
Bo Viscous drag term Nsm-1
Bo Viscous drag coefficient sm-1
Bt Transmission losses viscous term
Bu Viscous undriven wheel drag Nsm-1
C MIRA wind tunnel cross-sectional area m2
Co Velocity squared drag term Ns2m-2
Co Coefficient of drag
Co 0 Coefficient of drag at zero yaw angle
CL Coefficient oflift
CL 0 Coefficient of lift at zero yaw angle
CLF Coefficient of lift front axle CLR Coefficient of lift rear axle
Cp Pressure coefficient
CMX Rolling moment coefficients
. CMY Pitching moment coefficient
CMZ Yawing moment coefficient
Cs Coefficient of side force
Cs 0 Coefficient of side force at zero yaw angle
CSF Coefficient of side force front axle CSR Coefficient of side force rear axle
Cy Tyre slip coefficient N rad-1
a Velocity squared driveline drag coefficient Ns2m-2
D Basic aerodynamic drag force N
FA Aerodynamic drag force N
Fo Total drag force N
FOr Driveline losses N
FM Mechanical drag force N
xiv
Nomenclature
FR Tyre rolling resistance N
FT Tractive effon N
Fu Total undriven wheel drag N
Fw Drag force on a single undriven wheel N
fd Vane damped natural frequency Hz
fn Vane undamped natural frequency Hz
In Arbitrary function evaluated at n
in Derivative evaluated at n
Gfd Final drive gear ratio
g Acceleration due to gravity ms-2
h Integration step length s
h Differentiation step length
Iw Inertia of a single wheel kgm2
Iw4 Inertia of four wheels kgm2
la Gearbox inertia kgm2
KIl Coefficient to modify Coo for angle of attack rad-1
Ko Coefficient to modify Coo for yaw angle rad-2
KL Coefficient to modify CL" for yaw angle rad-2
Ks Coefficient to modify CSo for yaw angle rad-1
KT Tyre loss temperature correction factor deg K-l
kp Pitch stiffness coefficient Nm rad-1
I Characteristic aerodynamic length . m
L Lift force N
Lw Turbulence scale length m
Zp Moment arm for pitch due to acceleration m
I.n Mean vehicle length m
10 Overall vehicle length m
lw Vehicle wheelbase m
M Vehicle mass kg
M" Effective vehicle mass (including rotating inertias) kg
My Pitch moment Nm
m Number of data points in a single coastdown
N Yawing moment Nm
n Number of tests
p. Static pressure at anemometer location Pa
Pp Static pressure at tunnel pitot Pa
Pw Static pressure at mid-wheelbase Pa
xv
Nomenclature
P tot Total pressure Pa
R Rolling moment N.m
Rei Reynolds number based on vehicle length
Ry Tyre rolling radius m
S Aerodynamic side-force N
Tl Torque at left hand wheel Nm
Tr Torque at right hand wheel Nm
To Observed ambient temperature K
Ts Standard temperature K
Tt Tyre temperature K
s Sample standard deviation
t Tune s
t 't' statistic
v Vehicle speed ms·1
vr Total relative air speed ms· l
Vb Tunnel airspeed at end of boom ms·1
vh Ambient head wind ms·1
vrni Measured vehicle speed at point i ms· l
vci Calculated vehicle speed at point i ms·1
vp Reference speed at tunnel pitot static ms·1
Vw Tunnel airspeed at mid-wheel base ms·1
Vx . Ambient cross wind ms·1
V_ Freestream airspeed ms·1
XCp Position of lateral centre of pressure as % of
wheel base from C of G
XD nth order tyre drag coefficient
Yj dummy data point
L'.Cp Incremental change in pressure coefficient
L'.R Contribution to constant resistance due to slip N
z dummy parameter
z Dimensionless statistical deviation
x Vector of control variables
F(x) Function to be minimised
fj(x) Residuals at point x
a Vehicle angle of attack rad
xvi
Nomenclature
J3 Spatial wind variation parameter rad-1
X2 Chi squared
y Slip angle rad
e Track inclination rad
Ad Vane damped natural wavelength m
A." Vane undamped natural wavelength m
v Kinematic viscosity m2s-1
~ ·Vane damping ratio
p Air density kgm-3
cr Population standard deviation
cr 2 z Variance in parameter z
't Turbulence ratio
u Statistical degrees of freedom
'If Yawangle rad
co Wheel angular velocity rad-1
xvii
Introduction
Chapter 1 Introduction. Page.
1.1 Introduction. 2
1.2 Review of track test methods. 5
1.2.1 Coastdown method. 7
1.2.2 Steady state method. 10
1.2.3 European regulations. 11
1.3 Rig measurements of drag components. 12
1.3.1 Tyre testing. 12
1.3.2 Wind tunnel testing. 13
1.4 Review of chassis dynamometer calibration methods. 14
1.5 Accuracy of road load data. 16
1.6 Objectives of the research programme. 16
1.6.1 Development of a mathematical model. 17
1.6.2 Application of on board anemometers. 17
1.6.3 Application of a simulation program. 17
1.6.4 Comparison of coastdown and steady state torque methods 18
1.6.5 An advanced test system. 18
1
Introduction
1.1 Introduction.
To understand the complex behaviour of a road vehicle it is necessary to correctly identify
and measure all the parameters that affect its operational characteristics. One area to have
received considerable attention over recent years is the measurement of a vehicle's resistance
to motion (road load). The impetus for this work has come from the consumer who demands
a sophisticated car which must provide the correct balance of performance and economy, and
from greater public and government awareness of the dangers of atmospheric pollution. This
has led to a tightening of the emission laws, and the prospect of much more stringent laws in
the future. These demands have put pressure on vehicle manufacturers to improve their
products by reducing fuel consumption and toxic exhaust emissions; improvements which
cannot be made without test facilities enabling accurate measurement and simulation of the
road load. This thesis describes a detailed study into a number of test and analytical methods
which can be used to measure a road vehicle's drag characteristics while it is in its normal
operating environment Data determined using these tests methods are invaluable for accurate
performance simulation, chassis dynamometer calibration, the 'real world' assessment of
veilicle modificlltiQns and the location of excessive sources of drag in vehicle validation ! work. The principal objective of this work is to obtain accurate and detailed road load data: I
I. A Fo~d Esc~rt 1300L (1983)donat~.!>r!he F~rd motor company was used in the rese~hJ Methods of measuring the drag of a vehicle when it is on a test track have been in use for
many years, and although the basic methods are very simple there appear to be almost as
many different approaches as there are investigators. In general whole vehicle testing carried
out at a test track falls into two categories, the coistdown (or free deceleration) method, and
the steady state test. In the former the vehicle is allowed to freely decelerate between two
speeds under the influence of its resistance, and in the latter sufficient tractive effort is applied
to maintain the vehicle at constant speed.
The equation of motion for the vehicle travelling on a flat track is a simple application of
Newton's second law:
= M dv edt
1.1
Each of the basic test techniques is designed to eliminate one of the terms in equation 1.1 in
order to isolate the drag term. In coastdown the applied tractive effort is zero so the drag is
equal to the time rate of change of linear momentum (equation 1.2). For a steady state test the
2
I nrroduction
total vehicle drag is equal to the applied tractive effort because the acceleration is zero
(equation 1.3).
Coruulown =
Steady State =
dv -M
edt 1.2
1.3
Using the two basic test methods road load data can be obtained with various levels of detail
by refining the test techniques and analysis. The extracted data can be in the form of simple
performance parameters. or as a detailed breakdown of the sources of the drag. Deciding
which is the most suitable meth,od to employ for a particular application depends on the
speciflc requirements. but the general trend is towards extracting maximum information from
the measured data.
Simple measurements to describe a vehicle's overall drag may be used to compare
performance characteristics or for the calibration of a rudimentary chassis dynamometer. for
example:
Total coastdown time from 70 mph to 15 mph (110-24 kph)
Coastdown time between 55 mph and 45 mph (88-72lqih)
Power required at 50 mph (80 kph)
Drag force at 50 mph
Alternatively similar measured data may be subjected to a more rigorous analysis in order to
separate the aerodynamic and various mechanical losses. The first step is to establish a
mathematical model to describe the drag forces acting on the vehicle. It is the development of
a suitable form for this model that presents one of the major problems in road load data
analysis. The model developed in chapter 2 and used in the analysis of real data is shown in
a simplified form in equation 1.4. The first two terms describe the mechanical losses and the
term in v2 is the aerodynamic drag.
= 2
(Ao+ Bov) +COV
I Mechanical losses
Aerodynamic drag
3
1.4
Introduction
The analysis (in both coastdown and steady state) is designed to establish values for these
coefficients, referenced to standard conditions. The fmal values describe a vehicle's drag
characteristics and may therefore be compared with those of other vehicles, or with results
from the same vehicle in different configurations. In practice the total drag is made up from a
number of separate sources. These include the tyre losses, transmission losses, aerodynamic
drag (which varies with aerodynamic yaw angle) and un-driven wheel losses. The principal
objective of this work is to accurately determine all the different sources of drag acting on the
vehicle, using data gathered during track tests.
In practice it is difficult to obtain accurate road load data from measurements made at the test
track because of the lack of control afforded over the many parameters which influence the
drag. The most significant of these is the presence of ambient wind which includes both
spatial and temporal effects. Even when testing is carried out in low wind conditions errors
are introduced into the results unless the ambient wind is allowed for. To obtain accurate
results a continuous measurement of local ambient wind conditions is considered to be
essential. This requirement is verified by including realistic ambient wind effects in the
mathematical model developed in chapter 2 and by the application of an on-board anemometer
during the test programme.
Due to the difficulty of separating components of drag from test track data, methods have
been developed for making measurements under laboratory conditions. These techniques
isolate a component of the total drag and investigate it under controlled conditions, most
notable are wind. tunnels and rig testing of tyres. Both of these methods have been in use for
many years but data generated have been used only for comparative purposes and are not
necessarily a true reflection of the characteristics on the road because of limitations in the
laboratory simulation. The importance attached to absolute values of drag coefficients
(particularly by marketing groups to CDO) has resulted in many refinements to these
techniques in an attempt to develop tests that represent road conditions, but the correlation
between wind tunnels is still not well established [11.
Before entering into a detailed discussion of the advantages and disadvantages of the different
approaches to drag measurement it is necessary to make some general observations. A
principal objective is to develop an advanced drag measurement method for obtaining suitable
road load data from the. minimum number of tests. The method must therefore be adaptable
so that simple parameters (such as total drag at 50 mph) can be determined without
4
InrrodLU:tion
perfonning a large number of tests. To illustrate this point an example of the practical use of
track test methods is the comparison of a number of different tyre setS on a single vehicle. As
the aerodynamic drag can reasonably be assumed to remain constant from test to test the
analysis can be simplified, and the number of tests required reduced by fixing the
aerodynamic drag term. The tyre drag can then be investigated more quickly.
1. 2 Review of track test methods.
Within the two principal test categories of coastdown and steady state there are a number of
different methods of measuring the vehicle drag, these are summarised in table 1.1.
Vehicle drag measurement methods.
Method Description Coastdown
Advantages
Simple Coastdown time between Quick and simple approach coastdown two gates is measured
Disadvantages
Cannot be corrected to standard conditions.
FuIl Coastdown from maximum Total load is measured. Complex analysis. coastdown speed of interest to minimum Drag components can
be separated
Manifold vacuwn
Measurement of inlet manifold depression
Simple and quick, total Ina:curnte and losses are measured. lacks repeatability
Driveline torque
Wheel torque metelS
Strain gauges mounted on drive train
Bolt on torque transducers mounted in the driven wheels
Simple technique
Simple technique. Instrumentation is transportable
Table 1.1
Time consuming. Some losses are not recorded.
Expensive, Not always accurate. Some losses are not measured.
Some aspects of practical testing apply equally to all the test methods. The following basic
rules will help to minimise variation in the results.
i) The test track should be flat or the gradients known.
ii) During testing·the track should remain dry.
iii) If other vehicles are present on the track it should be ensured that they do not
5
Introduction
interfere with the testing. If the test vehicle passes or comes close to another vehicle
the test must be abandoned.
iv) Before testing commences the vehicle should be warmed up on the track at a chosen
steady speed, for a minimum of 30 minutes.
An important general consideration which also applies to all the methods discussed here is the
application of on board anemometers. The established methods of track testing do not use
anemometers at all, or at best use only track-side anemometers, and so they depend on
making the measurements when the ambient wind is low. The effects of wind must then be
neglected, or some averaging is performed by conducting the tests in opposite directions on
the track and performing a large number of tests. An example of the allowable wind
conditions is given by the EEC 88/436 regulations [2] ,these stipulate that:
"Testing must be limited to wind speeds averaging less than 3 ms-I with
peak speeds less than 5 ms-I. In addition the vector component of the
wind speed across the test road must be less than 2 ms-I."
Although the stipulated wind conditions are not stringent in tenns of the possible errors
introduced into the results, the limits themselves cannot be met for long periods of the year in
many European countries.
Non-anemometer methods were originally developed for measuring the total drag force and
not for separating it into its components, although they are now often used for this purpose.
The advantages of this approach are that the car can be tested in its market condition, and the
instrumentation required is simple and inexpensive.
Using on-board anemometers the total relative airspeed and aerodynamic yaw angle are
measured continuously throughout every test, so a full correction for the ambient wind can
then be made. The additional information provided by the anemometers allow the mechanical
and aerodynamic terms to be accurately separated. It is also possible, if there is a sufficient
range of yaw angles, to determine the variation of Co with yaw angle. Disadvantages of the
anemometer method are the physical presence of the instruments which alter the flow pattern
around the vehicle, and hence change the aerodynamic characteristics. The instrumentation
required is no longer simple, and the anemometer must be mounted securely on the vehicle
before testing can start .. Once mounted on the vehicle the anemometer must be calibrated as
the measurements are influenced by the presence of the vehicle.
6
Introduction
1. 2.1 Coastdown method.
In the coastdown method the test vehicle is driven up to a speed above the maximum of
interest, the gears are shifted to neutral and the vehicle is allowed to coast freely along the
track.§l During the deceleration phase the time rate of change of momentum is equal to the
forces resisting motion, as shown in equation 1.2. The term Me includes a contribution from
the rotating components and is therefore called the effective or equivalent mass. While the
vehicle is coasting the relevant variables are sampled and recorded for later analysis. In
general a number of tests are carried out to achieve an acceptable level of statistical confidence
in the results.
Apart from the differences between the mathematical models used to analyse measured data,
the variations within the coastdown method are primarily associated with the choice of
measurand and the method of analysis. The coastdown curve can be characterised using
acceleration, velocity, or displacement, an example of the corresponding time profIles are
shown in figure I.
U sing the acceleration method has the advantage of reducing the complexity of the analysis
procedure because the data can be directly applied to the equation of motion. Drag
coefficients can be extracted by correcting to standard conditions and fitting a simple least
squares quadratic function to the data. Unfortunately the low levels of acceleration
encountered during the coastdown make it difficult to achieve the required measurement
accuracy without recourse to expensive equipment such as a gyro-stabilised platform. The
method has been applied widely in the past (much of the original work having been carried
out by Roussillon(31) and is included in the ECE regulations, but its use is in decline.
Speed measurement during the coastdown is the most commonly used method because the
instrumentation is simple, cheap and widely available. The most obvious analytical technique
is to differentiate the data, and proceed as for the acceleration method, but in practice there are
a number of disadvantages associated with determining the derivative of experimental data.
By nature differentiation is a noisy process, and therefore a simple algorithm used with real
data is unlikely to yield consistent results.
§ 1 In the case of an automatic transmission an additional decoupling device is fitted to
disconnect the drive from the wheels.
7
Introduction
Lucas [4] suggests that the raw speed-time data should be fitted with a high order
polynomial. and the polynomial differentiated to obtain a smoothed force-speed
characteristic. This method is convenient and efficient but introduces another source of errors
as described by Emtage [5]. In particular it is suggested that the coefficients extracted from the
drag force-speed curve are very sensitive to errors in the high order curve fit. Figure 2
shows the characteristic pattern of residuals t 1 for real coastdown data which results when
the polynomial method is employed. These errors are introduced by the fitting of an
inappropriate model to the coastdown curve. They can be shown to be of a similar order of
magnitude as those due to crosswind effects on the aerodynamic drag coefficient.
There may be some advantage in the high degree of smoothing entrained in the polynomial
method of differentiation for a simple coastdown method. but it removes short period effects
such as ambient wind and is therefore of limited use when on board anemometers are
employed.
To avoid the problems of excessive smoothing and the application of an inappropriate
mathematical model a differentiation scheme using Lagrange polynomials can be used; the
three and five point formulae are given in equations 1.5 and \ 1.6 The success of this method
depends primarily on the accuracy of the input data and it perfonns well on perfect simulated
data. but in the presence of noise. errors are inevitably introduced.
= 1
2h (-/0+/2) (3 point) ',1.5
= (5 point) 1.6
§ 1 A useful tool in work concerned with curve fitting or the minimisation of a function is the
calculation of the residuals. They are generally defined as the "unexplained remainders" after
the application of all known principles. For road load data the residuals are the differences
between the observed values and those predicted by the regressed road load equation.
8
Introduction
To avoid the inherent problems of differentiation the coastdown equation can be analytically
integrated to obtain an expression for the speed-time function (Lucas [4]). The expression in
terms of speed and time can be fitted directly to the data using a parameter optimisation
routine (as first demonstrated by White [6]). For cases where the drag function cannot be
adequately represented by a quadratic in speed the integration can be performed numerically
within the optimisation process. This approach is used by Dayman [7] to consider non-linear
tyre characteristics.
If the third method of characterising the coastdown curve is used which requires that the
distance-time profile is recorded, the experimenter is faced with similar problems as with the
speed-time method. If the differentiation method is chosen the errors are amplified even
further because of the process of double differentiation. It is therefore recommended that the
mathematical model is integrated twice and a parameter optimisation routine used to extract
the coefficients.
Methods using anemometers are uncommon, Roussillon et. alJ8] used a Prandtl probe to
measure dynamic pressure allowing coastdown testing to be conducted in light winds at small
yawangles. Buckley et. al. [9], uses a method employing on board anemometers to determine
the aerodynamics of articulated lorries (where the influence of the anemometers are relatively
unimportant). The analysis considers the speed time data in overlapping 14 second bands.
Within each band the data are fitted with an exponential function and differentiated and the
ambient wind is averaged, the method was insufficiently accurate to determine all the losses
but by using tyre loss data obtained from the literature a value of Co was extracted, and
plotted against its corresponding yaw angle to generate a complete Co('I') characteristic.
Eaker [10] used a pressure probe and yaw angle indicator to determine the correlation between
track and tunnel Coo values. Losses other than aerodynamic were determined in separate
tests, and the variation of Co with yaw angle was measured in the wind tunnel.
In all of the coastdown methods described the drag measured by the basic test includes some
losses from the transmission as it is back driven. These will not be the same as when the
drive-line is transmitting torque, and are therefore referred to as the 'off-load' drive-line
losses in this thesis. To distinguish between these and other mechanical losses the drive line
drag must be measured separately. The preferred method is to measure the losses directly
during each test using appropriate instrumentation (such as wheel torque meters).
Alternatively if the instrumentation is not available they can be measured in the laboratory by
conducting separate coastdowns on the drive-train or un-driven wheels. If the latter method is
9
Introduction
used the losses must be determined as a function of speed and drive line oil temperature, so
that during subsequent track tests the correct losses can be calculated by monitoring the drive
line oil temperatureJl1]
1. 2 . 2 Steady state method.
In the steady state test the vehicle is driven at constant speed and some measure of the load is
recorded and averaged over a shon period. During steady speed operation equation 1.3
applies, as the drag is equal to the applied tractive effon. If the test is repeated at a number of
different speeds the complete characteristic can be determined.
Inlet manifold depression has been used as an indication of engine load for many years.
Vacuum gauges are often still used in vehicles to give an estimate of instantaneous fuel
consumption. Steady state methods depending on manifold vacuum are approved in the
relevant European regulations [2] as a method of measuring the drag on the road and setting a X certification dynamometer, however they are generally considered to be unreliableJl2] I \
Widespread use of the steady state method has come about with the introduction of accurate
and flexible torque measuring devices, in particular wheel torque transducers. The torque can
be measured at any point in the drive-train but it is imponant to consider which losses are
included in the measurement, (eg. wheel torque meters do not record any transmission
losses, but measurements by strain gauged drive shafts include the wheel bearing losses,
etc.). The principal advantage of wheel torque meters over other torque measurement in the
drive-train is that they can be quickly mounted on a vehicle, and may often be adapted to a
range of vehicles. Schiirmann et alJI2J made a comparison of available wheel torque meters
and obtained similar results for each unit. Steady state torque methods are now widely used
in the automotive industry, particularly for calibrating chassis dynamometers.
Analysing the acquired data is straightforward, as the measured data can be applied directly to
the mathematical model by simply averaging the measurements at each test speed and
performing a least squares curve fit. If the vehicle is not held at exactly steady speed, then it
is generally assumed that the acceleration is constant over the sample, and a simple
Newtonian correction is applied.
10
Introduction
1.2.3 European regulations
Homologation standards in Europe are regulated primarily by the EEC who publish the
minimum standards in relation to emissions and fuel economy required for vehicles to be sold
within the community. The current standard is EEC 88/436 [2] and is binding on all member
countries. Originally these regulations were developed by the Economic Commission for
Europe (ECE), a separate body sponsored primarily by the UN and voluntarily subscribed to
by 22 nations. The ECE Regulation No. ECE 15.05 was accepted in total by the EEC to
become 88/436, but they are more generally known in the automotive industry as the 15.05
regulations.
The 15 series regulations are concerned with the type approval of vehicles with regard to the
emission of pollutants and the reporting of fuel consumption data.' Approval tests are
performed using a certified chassis dynamometer which must be calibrated to simulate road
load using the prescribed procedures. Measurement of the resistance to motion on the road
must be conducted using the approved methods, contained in annex four of the regulation,
this section is summarised in appendix A.
Regulations of this type are generally a compromise between existing techniques and the
drive for improvements. The principal objective regarding chassis dynamometers was to
provide a road load measurement and calibration procedure which could be applied
throughout Europe. In view of the predominance of unsophisticated single parameter
dynamometers (Oayton water brake) the regulation had to be geared to this type of facility
and is therefore limited in its use to type approval testing.
~ Figures quoted in the press and in manufacturers data for the 'urban cycle' and steady state
56 mph fuel consumption are obtained using the methods prescribed in EEC directive
88/436.
11
Introduction
1.3 Rig measurements of drag components.
It is clear from the preceding sections that the measurement and separation of drag forces
using track test methods is not a trivial problem. Natural variability in the environmental
conditions, and the consequent difficulties of modelling the real complex situation have
prompted the development of alternative methods. The majority of these methods focus the
measurement process on a single area of drag, for example tyre test rigs for measuring the
tyre characteristics and wind tunnels for assessing aerodynamic losses.
Testing under laboratory conditions has the obvious advantage of affording control over the
test parameters. This in turn gives repeatability and the opportunity to study the influence of a
single test parameter in isolation. A disadvantage is the lack of realism in the simulation of in
service conditions, making interpretation of the results difficult. Modern test rigs are being
developed to provide a more realistic test environment, but these still often have
disadvantages which are discussed in the following sections.
In many cases the lack of realism in the laboratory tests is not considered to be a serious
problem. Data generated from the rigs can be used to provide valuable insight into the trends
associated with particular test parameters, or as a means of comparison between different
vehicles or tyres.
1.3.1 Tyre testing.
Tests on tyres to assess their rolling resistance have been conducted for almost as long as the
car has been in existence. J.D.Dunlop demonstrated as early as 1888 the fact that his
pneumatic tyre took less effort to rotate than its solid counterpart [141. This was shown by
rolling solid and pneumatic bicycle tyres in the courtyard of his Belfast workshop. "The solid
tyre wobbled and fell over before completing the course whilst the 'pneumatic' propelled by
approximately the same force, travelled the length of the courtyard and rebounded vigorously
from the distant wall." Although crude, this test was sufficient for the racing cyclists of the
day to quickly adopt the new type of tyre.
Modern tyre test rigs fall into two categories, the drum rig and the flat belt rig. The most
common is the single roll, or drum machine. Torque or power measurements are taken for
two conditions, the tyre just skimming the drum, and the tyre under its test load. The
12
I ntrodlU:tion
measurement from the skim test is subtracted from the loaded condition to give the rolling
loss. It is accepted that significant differences in tyre behaviour are induced by the curvature
of the drum so the values obtained are not those that would be experienced under road
conditions, an empirical correction is therefore sometimes applied to the measured data. The
correction normally involves using the flat plate load required to give the same tyre deflection
as measured during testing on the drum as the divisor in determining the tyre rolling
resistance coefficient, instead of the actual test load. This compensates for the higher
hysteresis losses induced by the drum curvature [15]. Flat belt test machines have the
advantage of providing a flat test section, but the friction and windage of a belt system is
much higher than for a single drum so much greater measurement accuracy is necessary to
separate the tyre and machine losses. A standardisation of rolling resistance measurements on
both types of machines agreed in the automotive and tyre industry has generally restricted
laboratory tests to steady state temperature and free rolling conditions [16]. The amount of
data on the transient rolling resistance is therefore very limited.
To overcome some of the problems of simulating in service test conditions the 'shrouded
trailer' method has been developed by MIRAJ17] A test vehicle is completely enclosed in a
box and then towed by another vehicle at steady speed. A force transducer located between
the box and the test vehicle provides an estimate of the tyre losses. The test does not eliminate
the aerodynamic losses associated with the rotating wheels, and includes some bearing
losses. This method is cumbersome and has not therefore been widely adopted.
1.3.2 Wind tunnel testing.
Full scale wind tunnel testing has been in use for some 50 years as a means of developing
vehicle aerodynamics, testing engine cooling and comparing vehicle designs. Much of the
initial testing was performed in tunnels designed for aeronauttcal work, but the first purpose
built full-scale automotive tunnel was commissioned at MIRA as early as 1960. For most
comparative development work the 'quality' of the air flow is not significant but when
simulating the aerodynamic forces it is important to represent the actual air flow around the
vehicle as closely as possible, because the forces and moments represent an integration of the
pressure field over the vehicle. Discrepancies in the local flow velocity can cause significant
errors because the pressure is proportional to velocity squared.
A number of different tunnel designs are in operation throughout the industry, including open
13
Introduction
and closed test sections, with open (Eiffel) or closed (Gottingen) returns. Each arrangement
exhibits its own advantages and disadvantages, but limitations to the airflow simulation are
inevitable. Flow distortion, which affects the pressure distribution, is caused by the physical
size and type of the operating section (termed blockage). In a closed section the streamlines
are forced closer together, and in an open section they widen out, causing (respectively) an
increase or decrease in the approach velocity and the measured coefficients. Buoyancy effects
are encountered in closed section parallel sided tunnels (longitudinal static pressure gradient)
causing a small increase in the measured drag.
Relative motion between the road and the vehicle and wheel rotation are simulated only in
model tunnels. In full scale facilities the floor of the test section is taken to represent the
ground and the wheels are stationary. The boundary layer that forms on the floor of the test
section therefore results in a different flow field than is experienced on the road. The net
effect on the aerodynamic forces depends on the geometry of the vehicle.
The importance attached in recent years to absolute values for the coefficients (in particular
CDo) by manufacturers and the press have made it essential that coefficients obtained are
accurate, and comparable from tunnel to tunnel. Carr [1] shows that the correlation between
five full scale wind tunnels is sufficient only for general engineering purposes. Correction
techniques have been developed to account for blockage and buoyancy, and efforts made to
reduce the effect of the ground boundary layer.
1.4 Chassis dynamometer calibration methods.
An important application of road load data is in the calibration of chassis dynamometers. The
object of the calibration is to simulate the tota1load experienced by the vehicle on the road at
any given speed, such that the vehicle power unit is subjected to the same loads as are
experienced in service, in respect of the resistance to motion and the inertial loads.
Ideally total resistance as a function of speed is required for the calibration so it is not
intrinsically necessary to separate the measured data into the individual contributions such as
aerodynamic losses and tyre losses as described in earlier sections of this chapter. However
if the data are to be corrected to standard conditions then the individual contributions must be
modelled and separated so that the relevant corrections can be applied
14
Introduction
Calibration techniques used in vehicle homologation are covered in appendix A, [2] these
were designed for use with basic forms of dynamometer, and consequently have a number of
drawbacks. The adjustable characteristics of the dynamometer power absorption unit are
assumed to be related to the cube of the vehicle speed to provide simulation for the absent
aerodynamic power. Mechanical drag on the road is assumed to be equal to the sum of
internal friction of the dynamometer and the resistance of the tyres on the rolls. The main
objection to this method is the setting of the dynamometer at a single speed point, because
dynamometers which absorb the same amount of power at the set speed may differ markedly
at other speeds.
Further inaccuracies are introduced at the set speed point if the manifold vacuum method is
used to set the dynamometer. Schiirmann et.alJI2] report a variation of about 25% in the
dynamometer load setting for different drivers using the same road vacuum value. Using a
measurement of the driving torque however they were able to show a variation of only 3%.
Alternative methods allowed in the EEC regulations [2] include the setting of the power
absorption unit to repeat either a measured torque at a steady 50 kph, or a time to freely
decelerate from 55-45 kph. These methods are more repeatable but the inherent problem of
setting the power absorption at a single speed point remains. Schiirmann et.a!. [12] proposed
an alternative method of calibrating single parameter dynamometers such as those specified in
the homolagation regulations. By setting the dynamometer at two speeds (40 and 80 kph)
with defined tolerances, the author claims that an overall improvement in the accuracy of the
simulation can be achieved.
Modem D.C regenerative dynamometers of the type installed by Brush Electrical Machines at
Loughborough University can be calibrated to simulate the road load throughout the
operating range of the test vehicle. The calibration can be performed using a similar technique
to those proposed in the regulations, or extended to cover the complete speed range. Data for
a sophisticated dynamometer can be supplied as basic drag coefficients from which the
calibration is performed, or as corrected total drag against speed. It is important to ensure that
the components of drag included in the calibration data are compatible with the calibration
method. It is therefore recommended that the same test method is employed during calibration
as was used to determine the characteristics on the road. Commonly used methods of this
type are; matching the wheel torque meter measurements on the dynamometer with the
corrected results from the road, or matching the coastdown profile on the dynamometer with
a corrected road coastdown.
15
Introduction
1.5 Accuracy of road load data.
Estimating the accuracy of road load data, or ensuring that measured data are of a sufficient
standard is a difficult problem. EEC regulations require that a stated statistical test is satisfied
when applied to the measured coastdown times or mean torque values, the criteria for
acceptance of data is that the overall statistical accuracy is better than 2% at the 95%
confidence level.
The relationship between the accuracy of the acquired data and the accuracy of the measured
coefficients is addressed by Emtage [5l. It is suggested that the accuracy of the coefficients is
directly proportional to the RMS curve fining error, which arises primarily from random
sources, ie. measurement noise, wind fluctuations etc. Improving the accuracy of the
measurements reduces the RMS error and consequently improves the accuracy of the
coefficients. Correcting for localised ambient conditions using measurements made using on
board anemometers should improve the accuracy.
1.6 Objectives of the research programme.
Many of the limitations of existing test methods have been discussed in this chapter. It is
therefore the primary objective of this research programme to develop sophisticated
techniques for determining the drag on a road vehicle from tests conducted on a track, and to
accurately separate the drag into its components. In order to develop these techniques it is
necessary to consider:
i) The development of a mathematical model to describe the vehicle drag forces in
the presence of ambient wind.
ii) The application of on-board anemometers to provide a continuous measure of
local ambient wind speed and direction.
ill) The use of a simulation program to validate the test procedure and software.
iv) The relative merits of the steady state and coastdown methods of testing, and the
comparison of results obtained.
v) The development of a flexible analytical procedure to allow mathematical models
of varying complexities to be used.
16
Introduction
1. 6.1 Development of a mathematical model.
Analysing road load data gathered on a test track requires a thorough understanding of all the
drag forces acting on the vehicle. Chapter 2 of this thesis develops a mathematical model
suitable for application to both steady state and coastdown data gathered in the presence of
ambient wind.
The model is developed primarily from the literature. Aerodynamic assumptions made in the
model are validated using test data obtained in a full scale wind tunnel.
1.6.2 Application of on board anemometers.
To eliminate the inherent errors introduced by ambient wind on board anemometers are used.
The following areas are investigated in their application:
i) The influence of the instruments on vehicle aerodynamics.
ii) The calibration of the instrumentation in the presence of the test vehicle.
iii) The influence of the instrument dynamic characteristics on the calculated results.
1.6.3 Application of a simulation program.
A digital simulation program has been written to generate realistic coastdown data which is
used for the development and validation of the analysis software. The program is used for the
following purposes:
i) Basic software validation
ii) Analysis of the effect of instrument dynamics on calculated results
iii) Effects of system and measurement noise
iv) Coefficient sensitivity analysis
17
Introduction
1.6.4 Comparison of coastdown and steady state torque methods
Although the main problem associated with track measurements of vehicle drag is the
variability in the environmental conditions, a further complication which occurs when making
a comparison of the different test modes is the different operating conditions to which the
vehicle is subjected. Even in a single test mode like the steady state torque method the
coefficients obtained depend on where the torque is measured in the drive· line. As the
measurement point moves back towards the engine output shaft more of the transmission
losses are included. A summary of the comparison between the two methods is contained in
reference [18] by the author.
In coastdown testing the total losses of the vehicle are measured including the drive-line
losses, however as the vehicle is freely decelerating the transmission is in the overrun
condition and at very low load. Under these conditions there is no evidence to suggest that
the drive-line losses are comparable to a 'normal' drive condition. Transmission losses under
these conditions will be referred to as the 'off-load' drive-line losses.
To compare the results obtained in the two test modes it is important that particular attention
is given to the drive-line losses. This has been approached by instrumenting the vehicle to
measure these losses directly in both test modes, so that in any subsequent analysis they can
be removed to generate main coefficients that are independent of test method. During the
steady state test the drive-line torque is measured at three points, the first motion shaft of the
gearbox is instrumented to measure engine output torque, and each of the driven wheels is
fitted with a torque meter. By comparing the total torque at the wheels with the engine output
torque we have an estimate of the transmission losses. In coastdown mode the same wheel
torque meters can be used to measure directly the off-load losses.
1.6.5 Development of an advanced test system
The result of the research programme has been the development of an advanced test
procedure based on the coastdown method, which is designed to establish values of the
standard drag coefficients, and in addition detennine the variation of the aerodynamic
coefficient with yaw angle.
While providing a sophisticated analytical method is important, it is also recognised that
18
Introduction
flexibility is necessary in real test applications. The software has therefore been designed to
provide that flexibility to the user. Prior to analysis the operator can define the problem to suit
the investigation being undenaken by constraining one or more of the drag coefficients to a
given value. By fixing a parameter the complexity of the problem is reduced and the
remaining coefficients can be determined with greater confidence and hence fewer tests are
required. The implications of constraining parameters is discussed, and suitable applications
highlighted.
19
Development of the Mathematical Model.
Chapter 2 : Development of the Mathematical Model. Page.
2.1 Introduction to the model 21
2.2 Mechanical contribution 22
2.2.1 Tyre rolling resistance 22
2.2.1.1 Normal load 23
2.2.1.2 Speed 24
2.2.1.3 Ambient temperature 26
2.2.1.4 Tyre conditioning 26
2.2.1.5 Inflation pressure 27
2.2.1.6 Applied torque 27
2.2.2 Drive-line losses 27
2.2.3 Other losses 29
2.3 Aerodynarrriccontribution 29
2.3.1 Basic vehicle aerodynarrrics 30
2.3.2 Origin of the aerodynarrric forces 31
2.3.3 Aerodynarrric drag 32
2.3.4 Aerodynarrric lift 36
2.3.5 Aerodynarrric side-force 37
2.3.6 Summary of the aerodynamic effects 38
2.4 Summary of the model 39
2.5 A simplified model 39
20
Development of the Mathematical Model.
2.1 Introduction to the model.
The equation of motion of a road vehicle ttavelling on a straight ttack may be written down
by applying Newton's second law.
Thlctive effort
Drag force
+
Inertial force
+ Mgsin9
Gravitational furce
2.1
Applied ttactive effort is equal to the sum of the force resisting motion, the force required to
accelerate the vehicle and the force required to overcome gravitational effects. The effective
mass of the vehicle Me is the sum of the actual vehicle mass and the inertia of the relevant
rotating components, including the wheels and the drive-train.
I = M+ W4 2.2
Test methods used to determine the drag forces are designed to eliminate some part of
equation 2.1. Assuming that testing is conducted on a level test track then in coastdown mode
the tractive effort is zero so the equation reduces to:
Coastdown = -M dv edt
The steady state approach eliminates the inertial force and the equation is written as:
Steady state =
2.3
2.4
When conducting simple tests to determine the total road load these equations may be applied
without further knowledge of the drag function. If more detailed information of the sources
of the resistance is required or if the total load has to be corrected to standard conditions then
the drag function must be specified. The main difficulty in obtaining a representative vehicle
model lies in establishing the characteristics of this drag force function. This problem is
addressed in the remainder of this chapter. Although their effects cannot be totally separated
21
Development of the Mathematical Model.
except in a simplified model the principal components of Fo(v) are the mechanical and the
aerodynamic drag:
= + 2.5
2.2 Mechanical contribution.
Mechanical drag, or chassis losses as it is sometimes known, is used as a 'catch all' term to
cover any of the contributions to the total not covered by the aerodynamic drag. The main
mechanical loss can be attributed to the rolling resistance of the tyres, and in some cases it is
considered to be the sole source of mechanical loss [5,6]. In practice there are a number of
other known sources of drag, of which the most significant are the losses within the
drive-train. Other losses are relatively small and can either be measured separately or
minimised by careful test procedure, these include bearing friction, brake drag and energy
dissipated in the suspension. The energy dissipated in the suspension was shown to be
negligible by Morelli et alJ191.
To give some impression of the relative magnitudes of these forces the approxiIpl!te_ percentage contribution at 50mph is shown in the table below. These figures are based on
the test results for the Ford Escon l300L discussed .in later chapters.
Source
Tyre rolling resistance
Drive-line losses
Un-driven wheels
Contribution
70%
26%
4%
Assuming that the only contribution is from the tyres can lead to significant error. In the
following sections a model to describe the mechanical losses during coastdown and steady
state torque testing is developed.
2.2. 1 Tyre rolling resistance
Before entering into a detailed discussion of the factors affecting tyre losses it is imporrant to
establish a clear definition of rolling resistance. Under free rolling conditions the tyre rolling
resistance is simply the torque required to roll the tyre divided by the rolling radius. If
22
DevelopmenJ of the Mathematical Model.
however the tyre is transmitting torque then slip occurs between the tyre and the road and so
this simplistic defmition no longer applies. A preferred. more general definition is that the
rolling resistance is the energy dissipated per unit distance rolled by the tyre, (Nm per m or
N).
The absorption of energy by the tyre can be attributed to three processes [20). Hysteresis
losses due to cyclic deformation of the tyre as it passes through the contact patch account for
approximately 85% of the total. Slipping against road friction accounts for a further 5-10%
and the remainder is due to aerodynamic losses. In track testing these latter losses are
included as pan of the general aerodynamic tenn.
As the bulk of the tyre loss is associated with hysteresis some of the basic properties of a
visco-elastic material will now be considered. Bearing in mind that the same material
response exists in a tyre this information is useful for interpreting tyre characteristics. The
interplay between temperature, frequency and loss modulus of a typical tyre compound is
explained in figure 3 [16). At constant temperature the materials loss modulus increases with
frequency, as the temperature increases the dependence on frequency reduces. At constant
frequency however the loss modulus decreases with temperature, strongly if the frequency is
high, less strongly if it is low.
Tyre rolling resistance is affected by normal load. inflation pressure, temperature, applied
torque, speed and track surface material, but in practical track testing there is a large degree of
interaction. To isolate the effect of a single parameter it is often necessary to conduct
controlled laboratory tests using tyre test rigs (these are described in section! 1.3.1 ).
2.2.1.1 Normal load
An increase in normal load results in an increase in tyre deflection and so in the hysteresis
loss. The rolling resistance coefficient is therefore defined as the ratio of rolling resistance to
normal load.
= 2.6
Using this definition the rolling resistance coefficient is non-dimensional which provides a
means of comparing tyres of any tYPe or size under any operating conditions.
23
\.
Development of the Marhemarical Model.
2.2.1.2 Speed
Tyre rolling resistance variation with speed is a typical example of the interaction of a nwnber
of different parameters to generate an overall characteristic. Considering the steady state
condition, (which is, as noted in section:1.3.1, the type of data reported in the bulk of the
literature) then at each test speed the the tyre temperature is allowed to reach equilibriwn and
the rolling resistance is measured. The shape of the rolling resistance I speed curve is
generally of the form shown in figure 4 [15,21]. The rapid increase above a particular speed
(which for convenience is called the break speed) is due to some high order term in the speed
relationship, this is considered in more detail later.
To explain this characteristic Barson [15] suggests that as both temperature and deformation
frequency increase with speed, but have opposite effects on the rolling resistance they are
largely counterbalancing, leaving only a small change in rolling loss with speed. This
explanation is consistent with the tyre material characteristics of figure 3. As the speed
(frequency) increases the loss modulus increases and hence the hysteresis losses go up but as
the tyre is rotating faster the heat produced per unit time increases so the temperature is
raised, causing a reduction in loss modulus. There is no compelling reason to asswne that the
sign of the residual effect is positive.
The approaches taken by researchers using track testing methods to model tyre loss speed
dependence varies widely, in some cases the speed dependent term is neglected and equation
2.6 is used [6,11]. The most common method though is to include a term which is linear with
speed [5].
2.7
The presence of an higher order term is shown by Smith et al. [22] by developing a simple
tyre model which demonstrated a v2 (equation 2.8) term arising from the tyre tread impact on
the road surface. A similar model is used by Yasin [23] based on a small sample of tyre test
data. The use of a v2 model can lead to problems in the data analysis because the
aerodynamic coefficient is dependent on vr2, and as the two terms are highly correlated they
may be difficult to separate.
24
Developme1l1 of the Malhemarical Model.
2.8
Dayman [7] shows that in coastdown testing the assumption of a constant rolling resistance
tenn distorts the values of aerodynamic drag. By using an arbitrary higher order term of the
fonn given in equation 2.9 it was demonstrated that reduced coastdown curve fit error
resulted. The 'best' value for b in equation 2.9 was found to be 4. Emtage [5] perfonned a
similar analysis and determined a value of 3.5 for b. In both cases the researchers chose to
ignore the drive-line losses and it is likely that this had a significant effect on their results.
= 2.9
Data so far presented are for equilibrium temperature conditions but in both the coastdown
and the steady state torque methods this situation is not reached because the vehicle is
'conditioned' at a single speed before testing proper starts. Literature on the effect of transient
tyre losses is very limited but the work by Schiiring [16] can be interpreted to give some
insight into the results from track tests. It is suggested in this reference that the rolling
resistance of a particular tyre at a given speed and tyre temperature is always the same
regardless of the 'path' by which the temperature is reached. In the case of coastdown testing
the vehicle is warmed up at a single speed, an effective step change in speed is inputted and
the car is then allowed to decelerate. It can therefore be assumed that the tyre temperature
throughout the test is determined by the speed at which the tyre was conditioned.
The effect on rolling resistance is best interpreted using figure 5 which is adapted from the
work of Schiiring [16]. The weak dependence of steady state rolling resistance on speed is
shown by the equilibrium line. Point A represents the condition reached during the warm up.
When conducting a coastdown test the speed is increased step-wise to the maximum of
interest (point B). As the vehicle decelerates it passes back along the line through the point A
to C because the relatively short time of the test ensures approximately constant tyre
temperature. When coasting from B to A the tyre temperature is below its corresponding
steady state temperature so the tyre losses are greater than those measured at equilibrium.
Below the conditioning speed CB to C) the reverse is true, so the rolling resistance is less than
for equilibrium. The method of conducting steady state torque tests produces a similar effect
because the tyre is conditioned at the same speed. It is therefore expected that during the track
tests the tyres will exhibit greater speed dependence than for steady state conditions. This is
at variance with the results of Ivens [24) who reported that steady state rig and tyre losses
25
Development o/the Mathematical Model.
measured in coastdown were both independent of speed, however it was demonstrated by the
author [25] that the coastdown analysis method used was flawed so this relationship between
rig and track measurements has not been established. The form of the equation chosen for
the analysis of measured data is as given in 2.7.
2.2.1. 3 Ambient temperature
Ambient temperature is an external effect imposed on the tyres which causes a direct change
in the tyre characteristics. If rolling resistance coefficients are to be compared they must be
referenced to a standard ambient temperature, the most convenient is to use the EEC
regulation conditions [21. Figure 6 shows the influence of cavity and ambient temperature on
rolling resistance coefficient [211. An approximately equal rise in cavity temperature results
from a rise in ambient temperature. It is suggested [161 that the relationship of rolling
resistance with tyre temperature can be written as an exponential of the form :
= 2.10
For small changes in Tt equation 2.10 can be approximated with a truncated Taylor series:
2.11
As the change in ambient temperature causes a proportional change in tyre temperature the
equation can be rewritten to include the rolling resistance speed model of equation 2.7, and
using ambient temperature to correct to standard conditions. The value of KT used is
O.OO86f'K.
= 2.12
2.2.1.4 Tyre conditioning
As the rolling resistance is dependent on temperature it is clearly important that the tyre is at
operating temperature before testing commences. Referring to figure 5 when starting from
cold at point A' the tyre is run at steady speed and the rolling resistance/temperature profile is
26
Development of the Mathematical Model.
defined by A' to A. The equilibrium condition at point A is reached after approximately 30
minutes running.
2.2.1. 5 Inflation pressure
The influence of inflation pressure on power loss in the tyre has been well established by
testing over the years. Increasing inflation pressure reduces the rolling resistance at all speeds
because the hysteresis losses are less at the lower tyre deflections. The literature [16.21]
indicates that an increase of 1 psi in inflation pressure typically reduces rolling resistance by
1.0 to 2.5%.
2.2.1. 6 Applied torque
The effects of braking and traction are shown in figure 7 [20]. The application of a driving or
braking force increases the longitudinal slip resulting in an increase in rolling resistance. This
effect is small unless the driving coefficient is comparatively large. In the case of a
coastdown the torque applied to the tyre is very small giving a driving coefficient of typically
0.02, in steady state mode the coefficient may increase by a factor of five to as !lluch as 0.1.
, (The driving c~fficie~t is definc:ct as the tractive force divided by the vehicle weight.)
2.2.2 Drive-line losses
Losses observed in geared transmissions arise from friction between the meshing teeth,
friction in the bearings and losses due to oil churning in the casing. These frictional effects
appear as a reduction in the transmitted torque and are a function of input torque, lubricant
viscosity and speed. Because the losses are generally small, particularly at low load they are
difficult to measure and model. It is suggested [26] that the losses are proportional to speed
and at low load the churning losses are dominant causing up to a second order effect with
speed.
Drive-line losses can be measured in separate'tests conducted in the laboratory [11], or during
track tests using torque meters [18]. In a laboratory test the vehicle is jacked up and a
'transmission only' coastdown performed. To calculate the friction torque the system inertia
must also be known. As the losses are dependent on oil viscosity and hence temperature, the
temperature must be monitored and laboratory drive-line data corrected to the actual
27
Develcpment o/the Mathematical Model.
temperature measured during the track testing. Alternatively the losses can be measured
directly during the track tests. it is then unnecessary to correct the data for transmission oil
temperature. In coastdown mode the wheel torque meters record the 'off-load' drive-line
losses. In steady state mode an additional torque transducer at the output of the engine is
required. so that the input to and output from the transmission can be compared. This
provides an estimate of the 'on-load' drive-line losses.
The direct measurement is the chosen method in this investigation for two reasons; the
configuration of the vehicle is identical for coastdown and steady state torque tests because
the wheel torque meters are employed during coastdown. this allows the results to be
compared; secondly the measured data can be used in the analysis without modelling. so
removing a possible source of error. The drive-line losses FDr(v) are simply added to the tyre
losses of equation 2.12 to give equation 2.13.
= 2.13
If the data is not used directly in the analysis then the function FDr(v) must be defmed. Ivens
[11] uses a linear form to describe the drive-line losses. with a constant term for the tyres.
Therefore in the analysis of steady state data from wheel torque meters a simple two term
drag equation is sufficient. The drive-line losses are given by equation 2.14.
2.14
This representation of the losses (with a suitable term to account for driveline temperature) is
widely used simply because it provides a reasonable fit with experimental data [11]. but the
understanding of the mechanisms behind the losses. particularly at low load. suggest that a
higher order term should be included. for example a quadratic with speed (2.15). The two
models (2.14 and 2.15) are compared in the results section.
= 2.15
28
Development of the Mathematical Model.
2.2.3 Other losses
Other sources of drag include those in the un-driven wheels which arise from bearing friction
and brake drag, driven wheel brake drag and suspension losses. U n-driven wheel losses are
a combination of brake drag and bearing friction and though small do make a significant
contribution to the total losses, this was illustrated in section 2.2. As in the case of the
drive-line losses these can be measured directly using wheel torque meters, or by conducting
a coastdown in the laboratory. The latter method was adopted because of the expense
involved in a second set of wheel torque meters, which must be accurate at very low loads.
The un-driven wheel losses are modelled as a linear function with speed (equation 2.16)
= A +B v 2.16 u u
Brake drag from the front discs is associated with rubbing of the braking elements, the pads
on a disc brake are permanently in contact with the disc and may make a significant
contribution to the total resistance. This can be eliminated by pushing the pads away from the
discs during testing.
The model is specifically designed for straight line testing on a smooth, level track so losses
attributable to suspension action or due to running the tyre at a slip or camber angle
associated with steering inputs can therefore be ignored.
2.3 Aerodynamic contribution.
It was argued in chapter one that it is important to continuously measure the ambient wind at
the vehicle. This additional information is only be useful if a satisfactory mathematical model
of the effects of ambient wind on the vehicle drag is developed. The principal influence is the
presence of a headwind or tail-wind (which can be accounted for without anemometers if the
wind is steady) but important effects such as variation of CD with yaw angle, the influence of
lift on normal axle loads, and for non-zero yaw angle the effects of side-force are also worthy
of consideration. In the following sections a model of the aerodynamic forces is developed,
and a simplified form proposed for use in analysing track data. Before embarking on a
detailed study of the particular aerodynamic forces which affect the track measurements it is
useful to have some knowledge of the general mechanisms which cause aerodynamic forces
and moments.
29
Development o/the MatheTTUltical Model.
2.3.1 Basic vehicle aerodynamics.
The external flow around a vehicle is governed by the body shape and the Reynolds number,
a dimensionless parameter which is a function of vehicle speed, the kinematic viscosity of the
fluid and the characteristic length of the vehicle.
VI 2.17 Re, =
~
v -For a particular body geometry entirely different flows occur at different Reynolds numbers.
The Reynolds number is the ratio of viscous to inertial forces, at low Reynolds numbers the
viscous effects dominate and at high Reynolds numbers inertia effects dominate, it is
therefore the parameter which characterises the behaviour of the flow. - - - - - - -- ~-.,.-
If the Reynolds number, based on the total length of the vehicle, is greater than about 1()4 the
boundary layer concept of flow is valid (for a car Rei> 1()5 above about 2 kph). This states
that, provided the flow remains attached to the wall the viscous effects in the fluid are
restricted to a thin layer next to the wall. This is known as the boundary layer. Within the
boundary layer there is a velocity gradient from zero at the body surface out to the value for
the inviscid flow some distance away from the wall. The pressure in the inviscid flow is
imposed on the boundary layer. The velocity gradient in a typical boundary layer is illustrated
in figure 8.
Towards the rear of the vehicle flow separation occurs so that the boundary layer is dispersed
and a viscous wake is formed behind the vehicle. Flow separation takes place when there is
a positive pressure gradient in the direction of flow which retards the boundary layer,
generally caused when the body surface is inclined away from the flow.
To maintain constant aerodynamic forces over a range of Reynolds numbers the flow
separation point must be fixed at some position on the vehicle, for example at the top of the
rear window. If the separation point is not fixed then different wake sizes will occur at
different Reynolds numbers, causing undesirable changes in the aerodynamic forces. The
position of the separation point is governed by the state of the boundary layer. If the flow
within the boundary layer is laminar, separation will occur earlier than if the boundary layer
is turbulent The transition from laminar to turbulent flow depends on the Reynolds number.
During the track testing conducted in this work the minimum vehicle speed used is
approximately 5 ms-i , corresponding to a Reynolds number of the order of 106 it is therefore
30
DevelopmenJ olrhe Mathematical Model.
assumed that the flow is turbulent and the separation point is fixed.
In practice the flow patterns around the vehicle are not as simple as indicated here, separation
and reattachment of the flow may take place at several points on the vehicle, for example a
separation on the bonnet I windscreen and subsequent reattachment is shown as a separation
'bubble' in figure 8.
2.3.2 Origin of the aerodynamic forces
If a velocity gradient is present in a viscous fluid at a wall, as in the case of the boundary
layer, then a shear stress acts everywhere on the surface of the body. The integration of the
corresponding force components in the free· stream direction gives the friction drag and in the
absence of flow separation this is the main contribution to the body drag.
In the case where flow separation occurs, as it does for a bluff body such as a road vehicle,
the drag characteristic is quite different. The pressure distribution around the vehicle is
considerably altered from the theoretical inviscid condition as the separation leads to a large
area of low pressure at the rear of the vehicle known as the wake. Integrating the force
components in the free-stream direction resulting from the pressure distribution gives the net
pressure drag.
The total drag is the sum of the friction and pressure effects. For a road vehicle the pressure
drag is the predominant effect because of the large area of low pressure present in the wake.
(This highlights the need to fix the flow separation point on the vehicle to ensure a consistent
wake and therefore constant aerodynamic characteristics.) The drag coefficient is obtained
from the total drag and is based on the free-stream dynamic pressure, and the reference area
(projected frontal area).
Drag D 2.18
In addition to drag, other forces and moments occur on a vehicle and they are shown
schematic ally in figure 9. This figure shows the MIRA. convention with the origin at
mid-wheelbase, mid-traCk and ground level. Coefficients may be detemrined for these forces
and moments by analogy with the drag coefficient
31
Development of the Mathematical Model.
L 2.19 Lift CL =
1 y2A 1?-
Sideforce Cs S 2.20
= 1 y2A 1?-
Rolling Moment CMX R 2.21
= 1 y2A1 1? _ w
Pitching Moment CMY My 2.22 =
1 y2 A1 1? _ w
Yawing Moment CMZ = N 2.23
2.3.3 Aerodynamic drag
Aerodynamic drag coefficient is defined in equation 2.18, rearranging, the drag force is
written as:
D = 2.24
The most important contribution of the ambient wind is in the addition of a headwind or
tail-wind, which modifies the basic drag to:
D = 2.25
However, if the ambient wind vector also contains a crosswind component then it gives rise
to an aerodynamic yaw angle (0/), the relevant vector diagram is shown in figure 10. As the
flow field around the body is modified by the approach angle of the air stream the coefficient
of drag is a function of the yaw angle, a typical example of the characteristic for a car is
32
Development of the Mathematical Model.
shown in figure 11. The general representation of the drag force is given by equation 2.26.
Defining the drag coefficient in tenns of the total relative airspeed vr is the accepted standard.
D = 2.26
In the absence of a crosswind equation 2.26 reduces to the case quoted in equation 2.25. It is
useful at this stage to illustrate the errors that are involved when testing is conducted without
anemometers. Expanding the Co('V) characteristic into a zero yaw angle component and the
variation with yaw angle and expanding the relative airspeed term gives equation 2.27.
D = 2.27
Applying the normal assumptions used for a non-anemometer method but allowing for an
unknown wind in line with the vehicle as used by Ivens [11] (Ivens treats the unknown wind
in line with the vehicle as a variable which must be deternrined in the analysis) the equation
assumed is written as 2.28.
D = 2.28
In the case of the wind being in line with the vehicle, then equation 2.21 reduces to equation
2.28 and there is no modelling error, but in the presence of a crosswind the error can be
found by subtracting equation 2.28 from 2.27.
Error = 2.29
The first term of equation 2.29 is associated with neglecting the crosswind component effect
on vr. The second term comes from ignoring the variation of Co with yaw angle. When
extracting the coefficients (as in equation 1.4) these errors are not confined to the
aerodynamic term, but are distributed throughout all the coefficients. This is demonstrated for
coastdown data in figures 12 to 14, [25] these show the basic drag coefficients calculated
from coastdown data generated with a range of steady winds. In the 2 ms·1 crosswind
example the coefficients AD, BD and Co are in error by 5%, 5% and 1 % respectively, but the
33
Development of rhe Mathematical Model.
actual error in total drag at 50 mph is only 4.5 Nor 1 %. It must be noted that these are the
minimum errors that will be encountered. in the realistic case of non steady wind these errors
will be exceeded because the in line wind component will no longer cancel. It is clear that if
accurate separation of the mechanical and aerodynamic losses is to be achieved then on board
anemometry is essential.
Practical implementation of equation 2.26 to measured track test data requires a knowledge of
the drag function :
= 2.30
A number of alternatives are available to model the coefficient of drag against yaw angle.
Data measured in the wind tunnel can be used directly using linear interpolation to calculate
the value of toCo at any yaw angle. Or it may may be fitted with some arbitrary function (eg.
power series) which can be recalled during the correction procedure to generate a value of
toCo [5]. Alternatively a simple model proposed by Yasin [23] suggests that for small yaw
angles:
= ~o + 2.31
Yaw angles encountered while on the test track depend on the maximum allowable wind
conditions. For the EEC Regulations [2] the worse case encountered is the maximum
crosswind (2 ms· l ) and the maximum total vector (5 ms· l ) during a gust. The yaw angles
generated can be calculated for the headwind and tail-wind cases (figure 15). Large yaw
angles are only experienced at low speed in the presence of a tail-wind when the actual
aerodynamic drag generated is small. This simple model is suitable for the advanced
coastdown method as only a single additional term must be determined (Ko). If the advanced
method is not used then the value of Ko must be determined from wind tunnel tests.
Generation of a vehicle yaw angle is not the only phenomenon to cause variations in the
coefficient of drag. Angle of attack and the vehicle proximity to the ground. are both
effectively shape parameters which influence CD' The latter effect is dependent on vehicle
loading (which may also alter the vehicle attitude) but as all track testing is carried out at a
chosen reference condition this is not included in the model. Lift forces change the ride height
but this effect was assumed to be small and was therefore neglected. this assumption is tested
34
Development of the Mathematical Model.
in chapter 4. However lift force is impottant when considering its effect on the constant term
of the mechanical resistance, and is considered in Section 2.3.4.
Modification of Co due to changes of angle of attack (a) is another vehicle attitude effect. An
increase in the angle of attack (nose up) causes an increase in the drag. If the air-stream is
assumed to be parallel to the ground plane then angle of attack changes are only caused when
the vehicle deflects on its suspension. This can occur when the vehicle is accelerating and
decelerating due to weight transfer effects or due to the aerodynamic pitching moment.
The levels of deceleration experienced during a coastdown are characteristically small and
would result in maximum attitude changes of only 0.50 §. From the data presented in chapter
4 the aerodynamic pitching moment effect can be shown to be an order of magnitude smaller.
The wind tunnel test described in chapter 4 did not extend to measuring the a-CD
characteristics but they are fairly consistent from car to car for small angles of a [271. An
increase in a of 10 causes an increase in Co of about 4% (giving a value of Ka = 0.9 rad- l
for the test vehicle). As the effect due to the aerodynamic pitching moment is small it is
ignored, so the acceleration effect is modelled as :
= + Ka a
2.32
a is obtained from the vehicle deceleration, pitch stiffness (in N.m rad- l ) and the relevant
moment ann to give:
= + K a
2.33
§ Using vehicle suspension data, angles are obtained by considering the effects of
acceleration as weight transfer from one axle to the other, using the height of the C of G as
the moment arm; hence obtaining a pitch stiffness from the wheel rates of approximately
6Ox103 Nm rad-I.
(
35
Developmenl of the MazhernaticaJ Model.
Combining the effects of yaw angle and angle of attack (equations 2.30, 2.33)
= K I vM
aP 2.34
The full equation describing the aerodynamic drag tenn is obtained by combining equations
2.26 and 2.34, to obtain equation 2.35. This represents the basic aerodynamic drag but other
aerodynamic forces can also indirectly contribute to the total resistance.
= K I YM] 2 aP v
k r 2.35
P
2.3.4 Aerodynamic lift
Although the aerodynamic lift force was not considered to have a significant effect on the
attitude of the vehicle the reduction in suspension load decreases the nonnalload on the tyres,
reducing the rolling resistance. To include this in the mathematical model there must be some
i representation ~f the tyre drag term, it is considered to be a function of speed and of normal-I
1 ~oad_and is written as: .. __ . . _ _ __ _ ~
2.36
Including the lift force is straight forward as it can be interpreted as a change in the weight of
the vehicle:
2.37
substituting the full lift force from equation 2.19 :
= 2.38
36
Developmenl of the Mathematical Model.
The lift force is also dependent on yaw angle, the form of the function for a typical car is
shown in figure 16. Including the effect of the ambient wind vector as shown for the
aerodynamic drag in equation 2.26 yields equation 2.39.
= 2.39
The alternatives proposed for the implementation of the CL('V) function are similar to those
for the drag function above. Yasin [23] suggests that CL is also linear with yaw angle
squared:
= 2.40
2.3.5 Aerodynamic side-force.
In the presence of an aerodynamic side-force the tyre generates a slip angle [20]. The rolling
resistance is not significantly affected by the slip angle itself, but the component of tyre lateral
force in the direction of motion is included in the rolling resistance (figure 17). Assuming that
the side-force is reacted equally at each wheel the component of force in the direction of
motion at a single wheel is given by :
S tallY 4
2.41
For small slip angles the tyre force/slip coefficient Cy is linear and the slip angle can be
written as:
y = S
4C r
2.42
For small angles tan y= y, hence substituting 2.42 into 2.41 and allowing for all four tyres:
2.43
37
Develcpmenl of the Mathematical Model.
Expanding the aerodynamic side-force 'S' using equation 2.20 and including the effect of
yaw angle as in the drag and lift cases:
= 2.44
In this case the simplified version of the Cs('l') characteristic proposed by Yasin [23] suggests
that the side-force coefficient against yaw angle is linear for small yaw angles.
= 2.45
As the change in tyre loss is equal for positive and negative yaw angles the absolute value of
the side-force coefficient must be used in the vehicle model.
2.46
2.3.6 Summary of the aerodynamic effects.
A model of the main aerodynamic effects has been discussed and developed. It includes the
effects of ambient wind with respect to yaw angles and magnitude, and its effect upon the
aerodynamic force coefficients. The lift force is included in terms of reduction of axle load,
and the side-force for generation of drag forces due to slip angle. Vehicle angle of attack is
included where it is caused by vehicle acceleration. Equations 2.35, 2.40 and 2.46 are
combined to give the drag function of equation 2.47.
= [Mg- ~PACLMV;][FM(V)] + 4~ [.~,pAICs('l')lv;] y
+ 2.47
38
Development of the Mathematical Model.
2.4 Summary of the model.
The complete model of the drag function is obtained by combining equations 2.13, 2.16 and
2.47 _______ ~
=
+
+ 2.48
2.5 A simplified model.
The full model described above (2.48) is used in the digital simulation work covered in
chapter 6, where representative values of Ka, kp and Cy are used. In the analysis of track
data a simplified model may be used, which neglects small effects such as side-force and
angle of attack. The CD('¥) characteristic is included using the simple representation proposed
in equation 2.20.
=
+ 2.49
The equation of motion for the vehicle used for the analysis of coastdown and steady state
data can be written by substituting equation 2.49 and 2.2 into equation 2.1.
39
Development olthe Mathematical Model.
=
+
+ 250
40
Vehicle instrumentation and data acquisition.
Chapter 3 : Vehicle instrumentation and data acquisition. Page.
3.1 Introduction. 42
3.2 General Arrangement 43
3.3 Engine Torque Measurement. 43
3.3.1 Engine Torque Calibration. 44
3.4 Wheel Torque Measurement 44
3.4.1 Wheel Torque Calibration. 45
3.5 Vehicle Speed. 45
3.5.1 Vehicle Speed Calibration. 46
3.6 On-board Anemometry. 46
3.7 Temperature and pressure measurement 48
3.8 Data acquisition system. 48
3.8.1 Description of the Hardware. 48
3.8.2 Description of the software. 49
3.9 Summary. 50
41
- -- -~-- ~ -- -- --
Vehicle instrumentaIion and data acquisition.
3.1 Introduction.
Using the model derived in the previous chapter an instrumentation and data acquisition
system was developed to make measurements of all the relevant parameters. Instrumentation
to perform both coastdown and steady state torque tests is required but the system developed
is used in both modes, providing extra information and ensuring comparability of the data
derived from the two methods. Transducers are mounted on the vehicle to measure the
following parameters :
Vehicle speed
Torque in the two driven wheels
Engine torque (measured on the first motion shaft of the gearbox)
Total relative airspeed
Aerodynamic yaw angle
Ambient temperature
The required time base is provided by the computer
Apart from the engine torque measurement, the signals from all the transducers are used in
both test modes. In coastdown the primary measurements are speed, airspeed and yaw angle
against time, but an additional important measurement of the 'off-load' drive-line losses is
acquired from the wheel torque meters.
During a steady state torque test it is necessary to determine the torque transmitted by the
drive-line. Two measures are provided, the engine torque and the sum of the driven wheel
torques. These were chosen because they provide a measure of the transmission input and
output torques and hence the 'on-load' drive-line losses (or transmission efficiency). As in
coastdown testing the data from the on-board anemometers must be recorded.
Output from the temperature sensor and tyre pressures were recorded at the beginning and
end of each test.
42
----~ ----~--- ~-- --'
Vehicle instrumentation and data acquisition.
3.2 General Arrangement
Power supply requirements and source are important if noise problems are to be avoided and
a 24V DC supply was required for the computer. It was therefore decided to use conventional
car batteries as the source and isolate the whole instrumentation system from the vehicle
electrical system. A standard racking unit provided the basis for the conditioning unit with a
power supply module to provide bus lines for signal conditioning cards.
Signal conditioning cards are mounted in the rack including a card for wheel torque meters
and one for the anemometry although they have separate signal conditioning, these provide
power, and filter networks. The natural time constant of the coastdown test is very long (ie.
lOO seconds) and the frequency range of ambient wind at ground level is confined to less
than 1.0 Hz (peak power at 20 ms'! vehicle speed is at approximately 0.1 Hz) (28). All the
signals are therefore processed through 1.0 Hz cut off frequency Sallen and Keye second
order low pass filters prior to sampling by the analogue to digital convertor. A block diagram
of the entire instrumentation system is given in figure 18.
3.3 Engine Torque Measurement
Strain gauges mounted on the first motion shaft in the gearbox sense the torque at the input to
the gearbox. The gauges are mounted on a plain portion of the shaft 'downstream' from the
clutch spline, the engine torque is therefore measured after the smoothing effect of the
flywheel and clutch springs. Solid silver slip rings are embedded in a tufnel tube located on
an extension at the other end of the shaft so that they protrude through an aperture in the end
casing. The brush assembly is then mounted on the casing. Connection between the gauges
and the slip rings is via a centre drilling. Four gauges are arranged in a full active bridge to
minimise temperature drift and the noise associated with the slip ring sliding contacts.
Maximum contact speed at the brushes is approximately 4.0 ms-1 so standard silver/graphite
brushes are suitable [29]. Signal conditioning uses a standard strain gauge amplifier network
based on a low noise, low drift linear DC amplifier.
43
Vehicle instrwnentation and data acquisition.
3.3.1 Engine Torque Calibration
A static calibration was conducted using standard laboratory strain measurement equipment
with the shaft locked in a jig and a balanced beam to apply the load. The resulting calibration
curve of micro-strain against torque is given in figure 19. From the residuals in the curve fit
the accuracy is estimated to be iO.5Nm. After installation in the gearbox the on-board
instrumentation was adjusted by shunting one arm of the bridge with a calibration resistor
and adjusting the bridge voltage to give the correct output calculated from the original
torque/micro-strain calibration. A switchable shunt resistance can be used to periodically
check the calibration. (In calibration mode the bridge voltage should be adjusted to give
5.35V at the output.)
3.4 Wheel Torque Measurement
Transducers and telemetry to measure wheel torque were designed locally and built in the
Department of Transport Technology. The transducer consists of a two part bolt on unit
strain gauged to measure the torque. A schematic representation of the transducer is shown in
figure 20. The inner part is effectively a splined stub axle which bolts on to the wheel hub; an
outer section, in the form of a top hat, locates on to the splines over the end of the stub and
carries the road wheel. A roller bearing between the two parts prevents axial loads from
causing a bending moment in the strain gauged portion which is located outboard of the
bearing. Adequate sensitivity is achieved by 'thinning down' the tube section, where the
strain gauges are mounted
The signal from the strain gauges was amplified by electronic circuitry bolted to the
transducer and transmitted as an FM waveform via an aerial fixed to the tyre, a receiving
aerial located in the wheel arch is connected to a pre-amp to provide further amplification
before the signal is input to a receiver unit which demodulates the signal and performs a
frequency to voltage conversion. A schematic representation is shown in figure 21.
44
~ . ------ -- - - -- - --------- -- --- -. - ._-- ---- ----- ----- -- ----- -
Vehicle instrwnentation and data acquisition.
3.4.1 Wheel Torque Meter Calibration
Calibration was conducted by using a balanced beam and the electronics package described
above. After initial assembly a small variation in the zero offset was noticed when the
direction of applied torque was reversed. This was traced to side loading of the roller bearing
and was corrected by relieving the bearing fit to allow sliding during assembly. Original
calibration curves for the two transducers are shown in figures 22 and 23. A repeat test
conducted approximately 12 months later yielded similar calibration constants (b) as shovv~1 below. The (a) term represents the zero offset _. - - . - -_. -- -- - . _. ---
Test
1
2
a
5. 132E-2
3.568E-2
1
Torque meter No.
b
2.329E-2
2.322E-2
a
-2.708E-2
-2.282E-2
Where the torque is given by equation 3.1:
Torque =
3.5 Vehicle Speed
Qltput vohage - a
b
2
b
2.224E-2
2.224E-2
3.1
Instruments for measuring vehicle speed are available from a number of companies, the most
common type being a standard bolt-on fifth wheel. During testing, particularly at high speeds
the more basic versions can suffer from problems of bounce (ie. the wheel temporarily leaves
the ground). Sophisticated models have largely removed the problem using suspension
systems but this makes them bulky and expensive. An alternative known as the 'Corevit L'
uses a light beam pointed at the ground and a sophisticated electronics package to determine
the speed using a stochastic statistical analysis, the manufacturers claim exceptional accuracy
for the device but this system is also very expensive.
To obtain a measure of speed it was therefore decided to machine 128 slots around the
45
Vehicle insfrumemalion and data acquisition.
periphery of the brake disc and mount an inductive pickup on the brake calliper. This
eliminates the need for any additional external instrumentation which effects the airflow
around the vehicle. Each slot in the disc was filled with high grade silicon rubber to prevent
corrosion which could result in a poorly defmed signal. The output from the inductive pickup
is conditioned to produce a clean square wave signal which is used to trigger a frequency to
voltage convenor.
3.5.1 Vehicle Speed Calibration
In order to obtain a calibration the disc was mounted in a lathe and rotated over a range of
speeds, determined accurately using a digital tachometer, and the output voltage from the
signal conditioning recorded. The data obtained is shown in figure 24 with the best fit
straight line. The wheel RPM is converted to road speed using the dynamic tyre radius,
which is some value berween the static loaded centre height and the free un-deflected radius.
As practical measurements of the tyre dynamic radius are made on tyre test rigs, it is
important that this is carried out at the load and inflation pressure experienced in service.
Variations in the radius with speed are small (Typically an increase of 1 mm over the speed
range 60-120 kph [20] ) particularly for the steel belted radials used on the test vehicle. The
value used in the speed calibration was obtained from the vehicle manufacturer from tests
conducted on a flat belt test rig. Combining the effects of non-linearity and changes in the
dynamic tyre radius the accuracy of the speed measurement can be assessed. The maximum
error at 3Oms-1 is estimated to be ±O.15ms-l .
3.6 On-board Anemometry
To separate the sources of vehicle drag from measured track data on-board anemometry has
been shown to be essential (chapter 1). The instrumentation used in this work consists of a
rotating cup anemometer to measure total relative airspeed, and a micro response vane to
measure yaw angle. A schematic of the instrumentation is shown in figure 25.
An important first consideration is the mounting of the instruments on the vehicle, the ideal
situation is to locate them such that there is no interaction berween the transducers and the
vehicle, in which case they will measure true airspeed and yaw angle. In practice this is not
possible to achieve so the instruments were mounted on a boom extending from the front of
46
Vehicle instrwnentalion and data acquisition.
the test car. The length of the boom, though not critical, was chosen as 1.5m; this avoids the
area of extreme disturbance immediately in front of the vehicle. The height of the sensors
above the ground is 0.7m, this is at approximately the geometric centre of the vehicle so that
the measured air is representative of the air through which the vehicle is travelling. The
chosen distance above the ground of 0.7m is also the height specified for track-side
anemometers in the European regulations [21.
A rotating cup anemometer is essentially a simple fIrst order sensor, for which the dynamic
performance is defmed in terms of a distance constant and the threshold speed. Distance
constant is defIned in simple terms as the 'distance' of air that must pass the sensor for it to
respond to 63% (ie I-lie) of the step change from the initial condition to the final condition
[301 and is analogous to the time constant. The threshold is the minimum speed at which the
anemometer starts to operate. For the anemometer used in these tests the following
manufacturers data applies. The specifIcation of the anemometers is included in appendix B.
Distance constant
Threshold
1.5 m
0.22 ms·1
The vane has a second order dynamic response for which the defining terms are the
undamped natural frequency and the damping ratio. However the manufacturers data for this
instrument quotes only the damping ratio and the distance constant. In the digital simulation
work discussed in chapter 6 this information is used in conjunction with additional data
measured in the wind tunnel to model the dynamic characteristics of the anemometers.
Damping ratio
Distance constant
0.4 1.07 m
It has been mentioned that in practical testing it is not possible to eliminate the interaction
between the vehicle and the instruments, it is therefore necessary to assess the influence of
the anemometers on the vehicle drag, and the effect of the vehicle on the measured data (ie.
the calibration of the anemometers). These two topics are covered fully in chapter 4 which
describes the wind tunnel tests.
47
Vehicle instrumentation and data acquisition.
3.7 Temperature and pressure measurement
Ambient temperature was measured using a shielded hand held thermocouple. Ambient
pressure was obtained from the proving ground weather station located at a distance of
approximately 600m from the test track. This data is provided as an average every 10
minutes. Data was also provided regarding wind direction and strength and was only used as
a means to compare conditions from day to day and to the European regulations [2] prescribed
conditions. It is quoted in the results section relative to the test vehicle for the approximate
time recorded during the test. Tyre pressure was measured using a hand held pressure gauge
which was cross calibrated with an accurate meter in the Department.
3.8 Data acquisition System.
The primary function of the on·board computer is to control the acquisition of the measured
data, but some analysis and reduction capability at the time of the test is a desirable feature. It
is the latter facility that makes the use of a general purpose micro-computer preferable to a
standard data logger.
Experience has been built up in the Department of Transport Technology in the use of DEC
based computers for remote data acquisition tasks, it was therefore decided to use a similar
LSI 11/23 satellite in the vehicle. Program development was carried out on a host
mini-computer (DEC PDP 11/34) and down-line loaded to the target system installed in the
vehicle. This arrangement forms the lower levels of a powerful hierarchical computer
structure used for program development, data acquisition, and final analysis and display.
(figure 26)
3.8.1 Description of the hardware.
The LSI based system is a compact design including the computer card cage and a 7" CRT in
a single 19" rack. Space is provided in the cage for six separate cards so that the system may
be configured as required by the user. A DEC LSI 11/23 fitted with the optional hardware
floating point arithmetic chip, and memory management provides the basic computational
power. Communication is via a four channel serial I/O board using RS 232 standard.
48
Vehicle instrumenlalion and data acquisition.
Memory requirements when testing are fairly high although only modest sampling rates are
required, two 128 kbyte CMOS non volatile memory boards are used for data and program
storage. Memory can be write protected using switches located on the board so that the
programs can be secured. The battery back-up circuit allows programs and data to be retained
when the main power is switched off. This faciliry was essential for travelling to and from
the test traCk so that the main battery supply could be conserved.
Data acquisition is performed by a software controlled multiplexed 12 bit analogue to digital
convertor. The card provides the capability to multiplex up to sixteen channels of single
ended or pseudo differential, or eight fully differential inputs into a high speed sample and
hold amplifier. Analogue to digital conversion uses a successive approximation 12 bit
convenor, and produces a full 16 bit sign extended word with a maximum sampling rate of
100kHz. A software programmable gain amplifier giving gains of 1,2,5 and 10 is available
to maximise resolution for a wide range of input signals. For an input Voltage range of±10V
the 12 bit ADC gives a resolution of 4.88m V / bit.
Timing of the data acquisition functions is carried out using a programmable clock card
giving a number of count rates and modes of operation. The card may be used to generate
interrupts upon which the" ADC carries out the sampling functions.
3.8.2 Description of the software.
The software used on the vehicle was designed for ease of use and a clear display of the
parameters being acquired. A manual describing the operation of the system and the details of
the routines used is given in appendix C so only the overall structure is described here.
Normal application of a satellite LSI involves writing a standard Fonran program and
building it into an operating system, but in the vehicle maximum space for data was required
so the large operating system had to be discarded, and the programs were all written in Macro
11 assembly language. Software for the vehicle therefore had to be able to perform all the
normal operating system tasks, as well as the acquisition and analysis functions. The primary
tasks performed on the vehicle are:
i) Interface with the user (Menu system)
ii) Communication with the host computer to load programs and transfer data after
49
Vehicle insfrumentation and data acquisition.
completion of a test session.
ill) HIe handling, and management of the memory.
iv) Check for operating errors.
v) Data acquisition.
vi) Online scaling and display of sampled data
A schematic. diagram of the software arrangement is given in figure 27.
3.9 Summary
A summary of the instrumentation is given in figure 28 which shows the measurands,
transducer types, signal conditioning and accuracies. It is important to note that the
calibration is of particular importance when measuring small effects such as driveline losses.
50
Wind Tunnel Tests.
Chapter 4 : Wind Tunnel Tests. Page.
4.1 Introduction 52
4.2 MIRA full-scale wind tunnel 52
4.3 Blockage and 'horizontal buoyancy' correction 53
4.4 Vehicle configurations 54
4.5 Wind tunnel results 55
4.5.1 Coefficient of drag 55
4.5.2 Coefficient of lift 56
4.5.3 Coefficient of side force 56
4.6 Validation of the mathematical model 56
4.6.1 Drag effects 56
4.6.2 lift effects 57
4.6.3 Side force effects 58
4.7 Calibration of the on-board anemometers 58
4.7.1 Tests in the Transpon Technology open section tunnel 58
4.7.2 Tests in the MIRA tunnel 59
4.7.3 Airspeed calibration at the test track 61
4.7.4 Summary 62
51
- ---- .---~------ -- ---~ --- ~ ~
Wind Tunnel Tests.
4.1 Introduction.
Wind tunnel tests were carried out to obtain data relating to a number of aspects of the
research. Full scale testing in the MIRA tunnel was conducted to obtain the aerodynamic
characteristics of the baseline and fully instrumented vehicle. The measured aerodynamic
characteristics are used to determine the influence of the external instrumentation and to
provide validation data for the mathematical model developed in chapter 2. The measured
drag characteristics can also be compared at a later stage with those detennined from test track
data
As the anemometer cannot be mounted on the vehicle where it will measure the true
freestream conditions calibration data were obtained during the full scale wind tunnel tests
and during tests in the Department of Transport Technology open section tunnel. Dynamic
characteristics of the rotating vane were obtained in the Department's wind tunnel and are
used in the simulation work described in chapter 6.
Final calibration of the airspeed instrument was performed using a technique developed for
use during track testing and is described in section 4.7.3
4.2 MIRA full-scale wind tunnel.
Full scale testing was carried out in the MlRA automotive wind tunnel installation at
Nuneaton. A schematic representation of the tunnel is shown in figure 29 [l]. The tunnel test
section is closed with parallel sides and a cross-sectional area of 34.9m2. The return circuit is
semi-open as the entire tunnel is enclosed in a large hanger. Aerodynamic force measurement
is via a six component strain gauge balance, mounted in a turntable to allow the vehicle to be
yawed with respect to the airstream. Dynamic pressure measurement is from a wall-mounted
pitot-static 6m upstream of the balance. Blockage and buoyancy corrections are applied using
formula developed by MIRA.
A number of exercises to correlate the results from different tunnels have been reported Carr
[1] describes the correlation of a number of tunnels and concludes that correlation is
satisfactory for engineering purposes but to ensure comparability for advertising purposes
standardisation of vehicle mounting, test conditions and blockage and buoyancy corrections
are necessary.
52
Wind Tunnel Tests.
4.3 Blockage and 'horizontal buoyancy' correction
A blockage correction must be introduced to account for the reduction in flow area caused by
the physical presence of the vehicle in the wind tunnel. The reduction in flow area caused by
the blockage accelerates the flow at the test section and increases the aerodynamic
coefficients. The correction used at the MIRA tunnel assumes that the effective velocity at the
test section (vc) is related to the velocity at the upstream pitot-static tube (vp) in inverse
proportion to the cross-sectional area of the airstream, (ie. an area ratio correction).
v c = 4.1
This formula has been shown to cancel out the effects of blockage at zero yaw angle, and
slightly under correct at other yaw angles [11. The percentage blockage is calculated using
equation 4.2.
Percentage blockage = [ (C ~ A) - 1 ] x 100 4.2
Horizontal buoyancy is generated by a static pressure gradient along the axis of the tunnel
caused by the growth of the boundary layer along the roof, floor and walls of the parallel
closed section. As the effective cross-sectional area of the tunnel is reduced, the flow is
accelerated and the static pressure falls accordingly. The difference in static pressure between
front and rear facing portions of the test vehicle leads to a small increase in the measured
drag. The buoyancy correction is only applied to the drag and pitching moment coefficients.
The static pressure gradient has been measured and is quoted as :
dCp
dx = -0.0028 ·1
m 4.3
The mechanism by which the drag is modified is that each element (t.A) of the projected
frontal area is subject to a pressure differential proportional to the longitudinal distance
between the front and rear facing surfaces at that point. To simplify the correction a
parameter has been developed to describe the shape of the vehicle (l"A,) where I,.. is the mean
length of the vehicle and I., the overall length. The correction is then made a function of
overall length. The parameter lnA, has been determined by the staff of MIRA for broad
53
Wind Tunnel Tests.
categories of vehicle (ie saloon, notchback etc).
= dC (I) __ PI...!!!. dx 0 I
o 4.4
For the broad category of saloon cars (1,Jl.,) is estimated as 0.8, and hence the reduction in
CD due to horizontal buoyancy is -0.009.
4.4 Vehicle Configurations
An Escon 1300L (1983) donated by Ford Motor Company is used as the test vehicle. Trim
level is standard with two additional door mirrors. In both wind tunnel test configurations the
vehicle was loaded with sand bags to achieve a similar ride height and attitude as at the test
track.
Configuration A The base vehicle (Figure 30):
Frontal area 1.83 m2
Wheel base 2.395 m
Front track 1.385 m
Rear track 1.430 m
Overall length 3.970 m
Blockage 5.53%
Configuration B Base vehicle plus the external instrumentation as required for the track
testing (Figure 31). The instrumentation includes: Anemometry mounted on a boom
extending 1.5 m in front of the car, with the centreline of the rotating cups and vane at 0.7 m
above the ground; wheel torque meters with the F.M. transmitter and power supplies. Use of
the wheel torque meters involves a small increase in the vehicle frontal area and front track.
Frontal area 1.85 m2
Wheel base 2.395 m
Front track 1.461 m
Rear track 1.430 m
Overall length 3.970 m
Blockage 5.60%
54
Wind Tunnel Tests.
4.5 Wind tunnel results
Testing in the full-scale wind tunnel was carried out using the vehicle in each of the two
configurations described in Section 4.4 over a yaw angle range of ± 25 degrees, in steps of 5
degrees. Output signals from the aerodynamic balance were averaged over a period of
approximately 60 seconds to eliminate the effects of turbulence in the freestream flow. Tests
to determine the coefficients were all carried out at a nominal air speed of 27.5 ms·!
(approximately 60 mph).
The results may be used over the speed range experienced during track testing if it is assumed I that the coefficients are constant over the range of Reynolds numbers which this implies. (see
section 2.3.1)
Results are shown in figure 32 for configuration A and in figure 33 for Configuration B.
Graphical representation of the force coefficients against yaw angle are shown in figures 34
to 36.
4.5.1 Coefficient of drag (Figure 34)
Configuration A
Configuration B
Coo
0.385
0.401 (+4.1%)
COOA (m2)
0.705 (base)
0.742 (+5.2%) (+instrumentation)
The basic shape of the Co against yaw angle curve is unaffected by the addition of the
instrumentation. Over the range of ±25° yaw angle tested, Co increases from the minimum at
0° by approximately 20% at 25°. In the instrumented configuration the drag coefficient is
increased by an approximately constant factor of 0.02 (~ 4%) over the base vehicle,
throughout the yaw angle range tested. The more representative CoA value is increased by
approximately 5%.
55
Wind Tunnel Tests.
4.5.2 Coefficient of lift (Figure 35)
Configuration A
Configuration B
CL = 0.290 o
CLa = 0.273
Inclusion of the instrumentation decreases the coefficient of lift throughout the yaw angle
range. The magnitude of the change is from ~CL = 0.0 ~ 0.025. The increase in the lift
coefficient over the range 0' to 25' is approximately 130% in both configurations. The shape
of the CL against yaw angle curve is basically unchanged by the addition of the
instrumentation.
4.5.3 Coefficient of side force (Figure 36)
In the case of a symmetrical car eso is nominally zero at zero yaw angle, this is true in both
configurations tested. Mounting the instrumentation on the vehicle has little effect on the side
force coefficient, the difference between the two test configurations being generally less than
1 % throughout the yaw angle range tested.
4.6 Validation of the mathematical model
The mathematical model developed in chapter 2 makes a number of assumptions and
simplifications about the aerodynamic characteristics of the vehicle in order to develop a
model suitable for use in the analysis of coastdown and steady state track data. Data acquired
in the full scale wind tunnel tests have assisted in the validation of these assumptions.
4.6.1 Drag effects
Equation 2.31 proposes a simplified model to describe the variation of CD with yaw angle.
This is repeated in equation 4.5
= 4.5
Using the data acquired in the tunnel tests the values of KD for the base and instrumented
56
-------- ---
Wind Tunnel Tests.
configurations can be detennined. The Co against 0/2 data is shown plotted in figure 37 with
the best fit straight lines for the ranges ±15° and ±25°.
Configuration A
Configuration B
±15°
(rad·2)
0.600
0.614
±250
(rad-2)
0.458
0.458
For the test configuration (B) the models generated using these values of Ko are plotted
against the actual data (figure 38). It is interesting to note how close the values of Ko
obtained in the two test configurations are, this confinns the SUbjective view (4.5.1) that the
basic shape of the Co(o/) characteristic is unchanged by the addition of the external
instrumentation. This form to describe the Co(o/) characteristic is used as the basis for the
advanced coastdown analysis.
It was also assumed in the development of the mathematical model that the effect of changes
in the angle of attack, due to the aerodynamic pitching moment, on the drag coefficient are
negligible (2.3.3). In the extreme condition of an airspeed of 30ms-1 and yaw angle of 5° the
pitching moment is approximately 70 Nm, the pitch stiffness of 60 x 103 Nm rad-1 gives an
angle change of less than 0.07°, and a consequent change in Co of approximately 0.25% [27).
4.6.2 Lift effects
As for the drag case a simple model of the CL(o/) characteristic is proposed in equation 2.40.
The fitted lift data is shown in figure 39 and yields the following values of KL :
KL
±15° ±250
(rad-2) (rad-2)
Configuration A 3.64 1.86
Configuration B 3.64 1.78
The model generated for the test configuration is plotted with the measured data in figure 40.
The effect of lift force in the mathematical model is confined to the reduction in normal load
on the tyres. For an airspeed of 3Oms-l and 5° yaw angle the lift force is approximately
57
Wind Tunnel Tests.
300N, causing an increase in ride height of approximately 3mm, the consequent change in
drag cannot be easily estimated and is therefore assumed to be negligible. The reduction in
normal load however represents approximately 2.7% of the total test weight and an equal
percentage reduction in the tyre rolling resistance, it is therefore imponant to include this
effect in the model.
4.6.3 Side force effects
The model proposed to describe the Cs(1jf) characteristic is given in equation 2.45. Referring
to figure 36 the best fit straight line gives a value of Ks=2.4 rad·1 for both configurations.
Additional tyre losses due to the tyres running at a slip angle indicated in equation 2.44 and
2.46 can be estimated for the case of vr=30 ms,1 and 1jf=5°. The side force generated is
200N, and using a value for Cy=25000N rad,1 [31] the estimated change in rolling resistance
~=O.4N. This represents approximately 0.25% of the rolling loss.
4.7 Calibration of the on-board anemometers
The calibration was conducted in a number of stages. Initial checks on the manufacturers
calibration were conducted in the Transpon Technology open section tunnel, and full scale
work with the instruments mounted on the vehicle were conducted at MIRA. Final calibration
was performed using methods developed at the test track.
4.7.1 Tests in the Transport Technology Open Section Tunnel
First stage calibration work was carried out in the Transpon Technology open section, closed
circuit tunnel, to check the manufacturer's calibration of the cup anemometer, and to
determine the dynamic characteristics of the cup anemometer not quoted in the manufacturers
specification.
The airspeed calibration obtained for the cup anemometer is shown in figure 41. Tunnel
speed was calculated from the permanently installed pitot-static. The manufacturer's
calibration correlated well with the measured data.
58
Wind Tunnel Tests.
The vane was tested over a range of airspeeds to detennine approximate data for its damped
natural wavelength for use in the simulation work of chapter 6. A step input was generated
by displacing the vane tail through approximately 3()o and releasing it The damped natural
wavelength was obtained by measurement from the traces on the x-y-t plotter, and the
undamped natural wavelength can be calculated using the quoted damping ratio of 0.4.
Airspeed
(ms· l )
11.0
17.2
24.0
~ (m)
5.16
5.24
4.60
4.7.2 Tests in the· MIRA tunnel
An (m)
5.36
5.70
6.23
0.4
0.4
0.4
Tests in the MIRA wind tunnel were carried out to establish calibration data for both
instruments over a range of yaw angles and tunnel speeds. The signals from the anemometry
were recorded using the on-board data acquisition system, and averaged over a period of
approximately 60 seconds. Tunnel airspeed is ,measured using the upstream pitot-static and a
blockage correction applied to detennine the airspeed at the test section (section 4.3). As the
anemometer is a significant distance upstream of the test section the blockage correction is not
appropriate, so the tunnel speed must be recalculated for the anemometer location by
reversing the correction. Rearranging equation 4.1 :
= 4.5
In addition the horizontal buoyancy effect described in section 4.3 causes an increase in the
speed along the tunnel which is not accounted for. The tunnel pitot-static is located 2.57m
upstream of the on board anemometers so the difference in pressure coefficient is :
6Cp = -0.0028 x: 2.57
= -7.2 x 10 -3
) 6Cp is the change in static pressure divided by the dynamic pressure at the pitot-static:
59
p - p • p
I 2 -pv 2 p
Wind Tunnel Tests.
Total pressure is constant, therefore :
p - p I 2 = -pv
tot P 2 p
and
P tot - p. I 2
= -pv 2 •
4.6
4.7
4.8
Subtracting 4.8 from 4.7 and substituting 4.6 in the result gives the buoyancy correction:
4.9
The two corrections of equations 4.4 and 4.6 can be combined to correct the quoted reference
speed back to the anemometer.
[
V (C-A)12 C C :J (I-~Cp) 4.10
Figure 42 shows the measured airspeed against tunnel airspeed at zero yaw angle, giving a
linear calibration constant of 1.107. However over a range of yaw angles tested the
calibration factor is not constant as can be seen in figure 43. The calibration constant varies
from a value of 1.069 to a value of Ll07. The mean value is 1.092. Using a constant
calibration factor the possible error in the calculated airspeed is approximately ±2%.
The vane calibration shown in figure 44 yields a linear calibration constant of 0.869.
Referring again to figure 43 the vane calibration data is plotted to show the variation in
calibration factor over the yaw angle range. The range of calibration constants is from 0.849
to 0.900, giving a possible error in the calculated yaw angle of approximately ±2.5%.
60
Wind Tunnel Tests.
The variations in the calibration factors arise from two sources, the first is due to the change
in the flow field around the vehicle, and cannot be avoided. The second is because the
airspeed anemometer and the vane are both positioned 280 mm off the vehicle centreline,
which causes asymmetry in the calibration data. This problem could be avoided by using a
combined airspeed and yaw angle anemometer which can be positioned on the vehicle
centreline.
4.7.3 Airspeed calibration at the test track
The wind tunnel tests indicate that relatively large correction factors are required for the
anemometers when mounted in front of the vehicle. To test the influence of the wind tunnel
on these results a calibration was carried out using the data measured during actual
coastdown tests. The coastdown tests are conducted in pairs with runs in opposite directions
so, if it is assumed that the yaw angle effects will cancel out, a calibration factor can be
estimated for each test pair by dividing the average vehicle speed by the average airspeed
determined over the two runs. This method provides a calibration factor which covers the
relevant speed range and range of yaw angles. As a check on the results the mean yaw angle
can also be determined, and should be zero. The results in table 4.1 each represent the data
from 3 pairs of coastdowns.
Airspeed calibration data from track tests.
Group Airspeed Mean yaw angle
1 2 3 4 5 6 7 8 Overall Std. dev
calibration (degrees)
1.0719 1.0821 1.0879 1.0804 1.0807 1.0751 1.0760 1.0903 1.0806 0.0063
Table 4.1
-0.193 -0.232 -0.124 -0.130 -0.100 -0.283 0.235 0.292 ~0.067
The overall calibration factor of 1.0806 determined on the track compares with a value of
1.092 from the wind tunnel tests.
61
Wind Tunnel Tests.
4.7.4 Summary
The research vehicle has been tested in the full scale wind tunnel with and without the
external instrumentation used during the tests on the test track. The coefficient of drag is
increased by approximately 4% by the addition of the instrumentation.
In order to obtain the actual freestrearn airspeed and yaw angle the anemometers have been
calibrated on the vehicle during tests in a full scale wind tunnel, and at the test track. The
calibration data shows some variation with yaw angle, but constant calibration factors are
used in this work.
Actual airspeed (v) = 1.0806 (Anemometer airspeed) 4.11
Actual yaw angle ('I') = 0.869 (Vane angle) 4.12
62
--- - -------~ ---. ---~-------
Test programme and analysis of results
Chapter 5: Test programme and analysis of results. Page.
5.1 Test Programme 64
5.1.1 Environmental conditions 64
5.1.2 Vehicle preparation 65
5.1.3 Test procedure 65
5.2 Summary of analytical techniques 66
5.3 Coastdown analysis 66
5.3.1 Integration scheme 67
5.3.2 Extracting the coefficients 68
5.3.3 Scaling 69
5.3.4 Estimating the accuracy of the coefficients 69
5.3.5 Aexibility in the analysis 69
5.4 Steady state analysis 71
5.4.1 Extracting the coefficients 71
5.4.2 Estimating the accuracy of the coefficients 72
5.5 Driveline losses 73
5.5.1 Coastdown 73
5.5.2 Steady state 74
5.6 Undriven wheel losses 74
5.7 Mean coefficients and overall accuracy 75
63
Test programme and analysis of results
5.1 Test programme.
Track testing was perfonned at the MIRA vehicle proving ground on the twin horizontal
straights. The track consists of two, parallel, dual carriageway one mile straights linked at
both ends with banked curves, allowing some speed build up before entering the straight
portions so that the maximum speed reached during the tests can be extended. The track is
nominally level over its length but no survey has been conducted since its original
construction in 1965. It was apparent during a visual inspection of the track surface that some
local settling had taken place along the track causing small gradient variations, tests were
therefore conducted in both directions on the track to average the effects.
5.1.1 Environmental Conditions.
Apart from the ambient wind levels, the environmental conditions prescribed in the EEC
regulations [2] were adhered to during testing. In summary these are that the track should be
dry and the air density must not deviate by more than 7.5% from that at the reference
conditions of :
Ps = 100.0 kPa
Ts = 293.2 K
Prevailing conditions were obtained from the proving ground control tower in the fonn of an
average value for every 10 minute period.
In conventional testing the ambient wind levels must be limited to avoid excessive errors in
the results, the limits set in the EEC regulations are :
Average wind speed
Peak wind speed
vw = 3.0 ms·\
v = 5.0 ms·\ wp
Maximum crosswind component Vx = 2.0 ms·\
During testing conducted with on board anemometers it is unnecessary to limit the ambient
wind to these prescribed conditions.
64
Test programme and analysis of results
5.1. 2 Vehicle preparation.
For homologation testing conducted in accordance with the EEC regulations the vehicle
should be prepared using the manufacturers specification. The details of this part of the
regulation are given in appendix A section A.2.3. During the testing conducted for this
research it was not possible to adhere to these specifications because of the use of externally
mounted instrumentation. The effect of the instrumentation is to alter the aerodynamic
characteristics, and increase the front track of the vehicle by approximately 70 mm. The
combined effect of the wheel torque meters and the anemometers on the aerodynamic drag
has been shown (section 4.5.1) to be an increase of approximately 4% in CDO over the
baseline vehicle.
The same configuration for the test vehicle was used in every test to minimise variation in the
results, this gave an all up test mass of 1125 kg.
5.1. 3 Test procedure.
During a pilot study a practical test procedure was developed for collecting coastdown and
steady state data. The following procedure applies to both types of test
i) Cold tyre pressure is set according to the manufacturers instructions, and the
front disc pads released to eliminate unpredictable parasitic drag.
ii) The vehicle is weighed on the MIRA weigh-bridge in its test configuration
and the mileage trip set to zero.
ill) Vehicle conditioning is carried out at a constant 50 mph for 30 minutes.
iv) With the vehicle stationary on the track all instrumentation is appropriately
zeroed.
v) A single test block (defined below) is conducted.
vi) The mileage trip reading is recorded.
vii) Steps v and vi are repeated until all the required test data has been collected
viii) The vehicle is weighed a second time and the mileage trip reading recorded.
A block of coastdown runs consists of 6 tests, 3 runs being conducted in each direction. In
the event of any other vehicle, which may be using the track, interfering with the conduct of
the test that particular run and its pair are discarded. In general a block of coastdown data
takes approximately 30 minutes to collect
65 -------~
--~-- - ---- -- -----
Test programme and analysis a/results
A group of steady state runs consists of tests at 20, 30, 40, 50, 60 and 70 mph, in both
directions on the track. The full set takes approximately 40 minutes to perfonn.
5.2 Summary of analytical techniques.
Conventional methods of analysing the data from track tests have already been discussed in
chapter 1. In general these methods have been designed for the analysis of data acquired
without a continuous measure of the ambient wind, and therefore depend on the use of
averaging or smoothing techniques. When on-board anemometers are used these smoothing
methods are inappropriate because the bandwidth of the relevant infonnation has been
increased by the ambient wind data. The analysis methods described below have been
developed specifically for tests carried out with on-board anemometers.
5.3 Coast down analysis
The approach taken in the analysis of coastdown data has been to directly fit the equation of
motion of the vehicle coasting in the presence of ambient wind to the measured data, using a
parameter optimisation routine. In an application involving optimisation the object is to
minimise (or maximise) some function. This function is called the objective function. In the
case of a set of coastdown data the objective function is defined as the sum of squares of the
residuals; where the residuals are the difference between the measured speed values and'
speed values calculated using the coastdown model (5.1),
f.(x) I = 5.1
and hence the object is to minimise:
F(x) = 5.2
Where x is the vector of control variables. To summarise, the optimisation routine determines
values for the control variables (road load coefficients) which produce the best fit in a least
squares sense between the mathematical model and the measured data.
66
Test programme and analysis of results
The optimisation method has been applied to coastdown data by a number of researchers.
White (6) analytically integrated the coastdown equation to obtain an expression for the speed
time function, and arranged it into a suitable form to determine the relevant parameters using
optimisation code. A two term function was used to describe the drag, and the environmental
effects were not included. Emtage (5) used a three term representation of the drag function
including the effects of tyre temperature and a wind correction factor. The integration of the
three term quadratic function is shown in appendix D. To implement the ambient corrections
Emtage used a cumbersome differential approach which corrects the time interval between
consecutive speed points, to produce a 'corrected' speed time curve. This method can be
simplified by replacing the differential method with a simple simulation approach, but both
methods use only the initial estimate of the drag coefficients in order to perform the
correction, (this is to save computation time) and therefore have an in-built source of error.
To avoid this inherent error the method used here combines the correction procedure with the
optimisation, by integrating the complete coastdown equation using the measured ambient
conditions. The converged control variables determined by the optimisation algorithm are
therefore the drag coefficients referred to standard conditions. The associated accuracies of
the control variables are evaluated directly from information provided by the optimisation
process.
5.3.1 Integration scheme
Use of the analytically integrated expression of the coastdown equation (shown in appendix
D) limits the drag function to a quadratic. To facilitate the use of more complex drag
functions a numerical integration scheme has been implemented in this work.
Runge-Kutta 2nd and 4th order numerical algorithms have been tested for use in the analysis
software, by comparing their performance against the 'correct' analytical solution to a simple
quadratic drag function case. The level of agreement obtained using the 4th order
Runge-Kutta greatly exceeded that achieved using the 2nd order, giving agreement to 11
decimal places as opposed to 4, so use of this scheme should not cause additional errors in
the analysis.
67
Test programme and analysis of results
5.3.2 Extracting the coefficients.
A commercially available optimisation routine (E04FCF) [321 available in the NAG
mathematical subroutine library is used to detennine the control variables (or drag
coefficients). This is described as: "A comprehensive algorithm for fmding an unconstrained
minimum of a sum of squares of m non linear functions in N variables." This minimisation
algorithm is designed to generate a sequence of points from a starting point x(l), ie. x(2),
x(3), ... , which is intended to converge to a minimum of F(x) (equation 5.2). The sequence
of points is generated using an equation of the form of 5.3,
(hI) x = 5.3
where vector P(k) is the direction of search, and a(k) is a step length. The operation of the
algorithm itself is transparent to the user. The model is specified by supplying a subroutine to
calculate the residuals fi(x) which may be called as required by the minimisation algorithm.
The routine selected for this work allows control over a number of aspects of the optimisation
(in particular convergence tolerance), and outputs information which is used to monitor the
optimisation process, and to calculate accuracies. These aspects are covered in later sections.
The optimisation procedure can be summarised as follows:
i) Define the mathematical model used to describe the drag forces.
ii) Code the model into a subroutine which calculates the residuals. ie. it integrates
the coastdown equation using the specified drag form and the measured ambient
conditions to determine v ci(x) and hence fi(x).(equation 5.1 ).
ill) Set up optimisation parameters
iv) Call optimisation routine with start values for the control variables.
v) At exit from the optimisation routine check that convergence is satisfactory.
vi) Calculate accuracies and confidence intervals of the coefficients.
68
- - - -.,
Test programme and analysis o/results
5.3.3 Scaling
Correct scaling of the optimisation problem can have a significant effect on the performance
of the minimisation algorithm. It is recommended [32] that in a least squares problem ( as
considered here) the user attempts to satisfy two conditions. The variables should be scaled
so that they are all of approximately the same magnitude at the convergence point, and such
that a fixed change in any of the variables results in a similar change in F(x).
5.3.4 Estimating the accuracy of the coefficients
Using information output from the optimisation it is possible to calculate the accuracy of each
coefficient by exploiting the special nature of the least squares problem. A subroutine to
perform the required matrix manipulations is supplied in the NAG library (E04YCF) [32]
which outputs the estimated variance-covariance matrix C. The diagonal elements of C are
estimates of the variances of the control variables at the solution.
The accuracies calculated using this method are based on the error sensitivity of each
coefficient at the solution, assuming normally distributed random errors, which may not be
the case in curve fitting to coastdown data. They are therefore interpreted as a measure of the
uncertainty in that test, and not necessarily as a guide to the overall accuracy of the method.
To determine the overall accuracy a significant number of test must be considered and the
spread of results determined.
To avoid confusion, in this report the accuracy calculated from the optimiser is called the
standard error of estimate, and the spread of results from a group of tests is referred to as the
standard deviation.
5.3.5 Flexibility in the analysis.
To obtain the level of flexibility proposed in the objectives of the research programme (1.6.5)
the engineer collecting and analysing the coastdown data must be able to tailor the analysis to
a particular circumstance. The mathematical model used in the analysis of the coastdown data
is obtained by setting the tractive effort equal to zero in equation 2.50 to give equation 5.4.
---,-- ~----- 69 --- - - -------
Test programme and analysis a/results
+
+ Mgsin9 5.4
The parameters which may be determined from the coastdown data are shown in bold text.
Flexibility is achieved by allowing the operator to flx one or more of the four highlighted
variables at some specilled value. This method of flxing some parameters is referred to as a
constrained analysis. As the number of terms in the analysis is increased, each parameter is
determined with a lower confldence. It is therefore important for the operator to use the least
number of terms possible to suit the application, as the required accuracy can then be
achieved with fewer tests.
If a four term analysis is performed then the three usual three drag coefficients are determined
but in addition the term Ko which describes the variation of Co with yaw is entered as a
variable, the inclusion of this fourth term is a radical departure from conventional methods. If
this method is used it is no longer necessary to determine the Co(\jf) characteristic in a wind
tunnel prior to the track tests.
In the three term mode any of the four variables may be flxed. If the term Ko is flxed then the
method is equivalent to the standard three term analysis, with the addition of on-board
anemometers. The value for Ko must be determined from wind tunnel data as was
demonstrated in section 4.6.1. Alternatively the measured wind tunnel data can be used
directly by supplying the program with a look up table of ~Co against yaw angle values.
Simpler forms of analysis (eg. two term) can be used to explore a single source of drag. In
the introduction (1.1) the example used was a two term analysis where both Coo and Ko are
constrained so that the tyre losses alone are determined. This method is useful for comparing
a range of tyres. It is important to note that the results obtained are dependent on the choice of
values of Coo and Ko so the results should only be used for comparative purposes.
70 - ~ --- ---- -- - -- --- ---- ------- - --- --- -- ----- -'--- ----- - --- -- ---
Test programme and analysis o/results
5.4 Steady state analysis.
A complete steady state test group is made up from an ensemble of single speed runs. which
together cover the complete speed range of interest. Data in each speed run are corrected to
reference conditions. and the complete data group is fitted with a least squares quadratic
function to extract the drag coefficients. and calculate the accuracies.
5.4.1 Extracting the coefficients.
Substituting the required drag function into the equation of motion (2.1) and rearranging
gives equation 5.5.
F _ M dv _ MgsinB _ T edt
I 2 2 I 2 zi'A~(2vvh+Vh +vx ) + ~A6CD(1jI)vr
=
5.5
Tenns on the left hand side are the applied tractive effort (FT) minus the corrective tenns.
Equation 5.5 can then be rewritten in the fonn :
= 5.6
Parameters Ao. Bo and Co are determined from the least squares quadratic fit. and the
corrected drag coefficients are calculated from equations 5.7 - 5.9.
=
=
=
A o 5.7
5.8
5.9
71
Test programme and analysis of results
In steady state testing the inertial tenn is nominally zero, but in practice it is not possible for
the driver to maintain exactly the required constant speed. The best compromise during
testing was found to be achieved by approximately setting the required steady speed and then
maintaining a constant throttle pedal position. The inertial tenn must therefore be included in
the analysis as a corrective tenn (equation 5.5). Problems of differentiating measured data
were discussed in chapter 1 with reference to coastdown analysis. In the case of steady state
testing the polynomial method (section 1.2.1) may be used as it is only applied to a corrective
tenn, any errors introduced in the curve fit will therefore be negligible.
The driveline losses are not included in the steady state analysis as the torque is measured at
the wheels, this is consistent with the approach taken for coastdown data where they are
measured directly and separated from the other forces. The coefficients derived are therefore
directly comparable.
5.4.2 Estimating the accuracy of the coefficients.
Each of the data points (Yi) used in the determination of the drag coefficients has contributed
some fraction of its own uncertainty to the uncertainty in the final solution. Assuming that
there are no systematic errors which would introduce correlations between uncertainties, the
standard deviation of the detennination of a single parameter (z) is the root sum square of the
products of the standard deviation of each data point multiplied by the sensitivity of the
parameter to that data point
5.10
It is reasonable to assume that the errors which occur in track testing are instrumental and so
the standard deviations for each data point are equal, (ie. cri = cr). An estimate of the sample
variance can be obtained from the data using equation 5.11.
2 (J = 5.11
In the practical coding of the method the sample variance is either calculated directly using
this equation, or by expanding it out and using the sums accumulated to detennine the
72
Test programme and analysis o/results
coefficients. The fIrst method is preferable as it minimises round off errors. The derivatives
required in equation 5.10 can be evaluated by taking the derivatives of the simultaneous
equations which are solved to determine the coefficients.
5.5 Driveline losses.
One of the key issues in the comparison of coastdown and steady state test results is the
removal of the driveline losses from the coastdown data to obtain comparable values of the
main coefficients (AD. BD and COo). It was therefore essential that they were measured. Little
is known of the characteristics of transmission losses at the low loads experienced in the
types of test under investigation here, so a suitable model was not available from the
literature. They were therefore included in the coastdown analysis in their measured form.
Having identifIed a need to measure the losses it was decided to devote some time to studying
their characteristics. To complete the data being acquired, additional instrumentation to
measure engine output torque was mounted in the vehicle (described in section 3.3), so that
the 'steady state' losses could be measured and compared with the 'off-load' losses measured
in coastdown. The measured data was fitted to the empirical models of driveline losses
quoted in section 2.3.2.
5.5.1 Coastdown.
Driveline losses during coastdown were measured directly using the wheel torque meters. An
estimate of the total driveline drag is obtained from equation 5.12 :
FOr = (T\ +T)
Rr 5.12
It was not considered necessary to make a correction for the inertia effect of the rotating
components in board of the torque transducer as the inertia and accelerations are both small.
Raw driveline data is fItted with a straight line to estimate the parameters At and Bt of
equation 2.14. In addition the quadratic form given in equation 2.15 is used. The results
obtained are presented and discussed in chapter 7 and 8.
73
Test programme and analysis of results
$.5.2 Steady state.
Driveline loss in steady state is calculated by subtracting the total wheel torque from the
engine output torque. It is not necessary to correct the measured data as the difference is
required. The driveline loss obtained from a set of steady speed runs is fitted with a least
squares straight line and the coefficients At and Bt calculated as in the coastdown. The results
are discussed in chapter 7.
5.6 Undriven wheel losses.
Undriven wheel losses though small, were measured in a series of separate tests and included
into the model. In the case of the car used in these tests the undriven wheel losses accounted
for 3.7% of the mechanical losses and 1.9% of the total at 50 mph.
A separate coastdown test on each of the rear wheels was performed with the back of the car
jacked off the floor. An electric motor was used to drive the wheel up to the maximum test
speed and stabilise them for 30 minutes and then removed to allow the wheel to freely
decelerate. A record of the angular velocity against time was recorded and analysed
The equation of motion for the decelerating wheel is written as :
= 5.13
Rearranging and integrating between consecutive data points gives the mean drag over that
period.
5.14
Equation 5.14 is used to calculate the drag at each measured point in the data and the resultant
force is fitted with a least squares straight line to determine the undriven wheel loss
coefficients A, and Bu, as in equation 2.16.
74
Test programme and analysis of results
5 • 7 Mean coefficients and overall accuracy
Having obtained estimates of the coefficients and their associated standard deviations in a
number of separate tests a group average and overall accuracy can be calculated. The
principle of least squares is applied again to determine a best estimate of the mean value of
each coefficient, but in this case the variance attributed to the coefficients are not equal and
must therefore be included as a weighting factor in the analysis. The weighted mean of
parameter z is estimated according to equation 5.15,
~z 5.15 =
L~ cr.
I
and the uncertainty in the mean is calculated using equation 5.16.
cr2 = 1
5.16 J.1. L-7
cr. I
The standard error of estimate which is a reflection on the 'quality' of fit to the test data is
used in the results section to calculate least squares estimates of the mean using the weighting
method above. In addition the overall accuracy of the method can be assessed by calculating
the spread of results from a group of tests. Using the standard deviation it is possible to
determine the number of tests required to achieve a specific level of confidence in the results.
7S
Validation of analytical software
Chapter 6 Validation of analytical software. Page.
6.1 Introduction. 77
6.2 The simulation program. 77
6.2.1 Equation of motion. 78
6.2.2 Wind generation 78
6.2.3 Instrument and vehicle dynamics. 79
6.2.4 Superposition of noise. 79
6.2.5 The complete model. 80
6.3 Coefficient sensitivity analysis. 80
6.4 Summary of the simulated data. 82
6.5 Discussion of results from simulated data. 85
6.5.1 Four term analysis. 85
6.5.2 Three term analysis. 87
6.6 Anemometer calibration errors. 88
76
- - --- ---- - -----
Validation of analytical software
6.1 Introduction
By simulating a number of sets of coastdown data with known characteristics the analytical
methods described in chapter 5 can be validated, and their overall accuracy assessed. The
data were generated using a digital simulation program which integrates the coastdown
equation to produce a speed time curve. Each pair of coastdown runs generated (in opposite
directions on the track) is analysed using the software developed for use with 'real' data
acquired at the test track, the results obtained are presented in this chapter.
The simulation exercise should not be considered to be an exhaustive analysis of the method,
but rather as a guide to understanding the results obtained from real test data. The objectives
of the simulation can be summarised as:
a) Software validation.
b) Coefficient sensitivity analysis.
c) Influence of instrument characteristics.
d) Effect of system and measurement noise.
e) To investigate the effect of constraining the coefficients at their input values.
f) To demonstrate the effect of anemometer calibration errors.
Using known input conditions of ambient wind, temperature, drag coefficients and noise,
coastdown speed / time data can be produced in a controlled environment. Prior to the
simulation of a pair of coastdowns the following parameters must be specified :
a) Values of the basic drag coefficients AJ)o Bo, and Coo
b) Shape of the Co('!') characteristic (either by varying Ko, or by
implementing a non symmetric Co('!') dependence)
c) Input ambient wind, in terms of headwind, crosswind and turbulence level
d) Levels of measurement and system noise applied
e) Dynamic characteristics of the instrumentation
6.2 The simulation program
The simulation software has been developed using ACSL (Advanced Computer Simulation
Language), a commercial package designed to allow simple coding of any dynamic model
from its mathematical description, and to provide an environment in which the model can be
77 --.- -- -- - ---- - ----
Validarion of analyrical software
exercised. The program to generate coastdown data is constructed from a number of blocks
(figure 45) including the basic equation of motion, vehicle dynamics, generation of ambient
wind (including spatial as well as temporal variations), anemometer characteristics and a
noise generator.
6.2.1 Equation of motion.
The equation of motion used in the simulation is based on equation 2.50, the driveline losses,
undriven wheel losses, track gradient and the effects of ambient temperature on the tyre
losses were not included to simplify the analysis, and concentrate on validation and dynamic
effects. The equation of motion used in the generation of the majority of the speed / time data
is given by equation 6.1.
Mdv
edt = 6.1
The values of Me' M, g, Ao, Bo, Coo, p, A , CL('l') (generated from a look up table) and Ko
are known inputs to the model, the actual values of'l' and vr depend on the output from the
ambient wind generator. The Co('l') characteristic is in the simplified form of equation 2.31,
the value of Ko used is equal to that determined for the test vehicle in the full scale wind
tunnel (0.614).
6.2.2 Wind generation
Generating realistic wind conditions is the most difficult aspect of the simulation work. It is
important to consider both the time variations (turbulence) and spatial variations (often
encountered when part of the test track is shielded and another part exposed).
For the purposes of simulation the simplest form for the time variations is to use a model that
can be represented using differential equations, these can then be included as a block in the
simulation program. Such a representation is the Dryden spectral form which closely matches
power spectral density relationships found for ambient wind in investigations by the
aeronautical industry [33). The model is effectively a filter system to which band-limited
correlated white noise i's the input, and the output is a component of the wind. Appropriate
scale lengths <Lw) and turbulence ratios ('t) were used [28). A set of equations for the inline
78
Validation of IJIUliytical software
component and a set for the cross-track component are used in the simulation. As a result of
this approach the wind input is specified by the operator in terms of the mean headwind,
mean crosswind and the turbulence ratio. The standard deviation of the wind generated by the
simulation is determined by multiplying the mean wind speed by the turbulence ratio.
Spatial variations are included in a simple form by allowing them to vary linearly with
distance travelled along the track. This is best described by figure 46. At one end of the track
the mean wind speed is relatively high and at the other end it is low. The magnitude of the
variation along the track is determined by the value of ~.
6.2.3 Instrument and vehicle dynamics
. An important part of the simulation for an anemometry based method is the response of the
measurement system and its interaction with the vehicle dynamics. Practically this can be
visualised by considering the influence of a gust of wind. The anemometers have known
dynamic characteristics (first order for the airspeed and second order under-damped for the
yaw angle); when the gust occurs the output from the anemometrs is modified by these
dynamic characteristics. Considering the test vehicle; as the gust passes along the car the flow
pattern is modified and the aerodynamic forces change. This can be simply represented using
a first order system, where the time constant is based on the length of the vehicle and the
airspeed, as the airspeed increases the time constant is reduced. Considered in isolation these
two effects may be a source of error in the analysis, but in practice the effects of the
instrumentation and vehicle characteristics will cancel each other out to some extent if the time
constants are similar.
6.2.4 Superposition of noise
In real world testing there is the inevitable problem of measurement noise, which is included
in the simulation by adding random noise to the measured signals; The noise is assumed to
have a Gaussian distribution with known standard deviation and zero mean.
In addition to measurement noise it is likely that there will be noise associated with factors
not included in the analysis. This is system noise. Possible sources of system noise in
coastdown testing are track surface irregularities, suspension motion etc. System noise was
included by adding Gaussian noise to the input coefficients.
79
--- ----~- -----~ --- - - -- ~ ------
Validation of analytical software
6.2.5 The complete model
In the bulk of the simulation exercise the equation of motion used to generate the speed / time
data uses equation 6.1 which is based on the drag function given by equation 2.50. This
representation of the equation of motion which uses a simplified description of the drag
function is also used to analyse real data acquired at the test track. To assess the likely errors
incurred by using the simplified model to analyse real coastdown data, a number of cases
were simulated using the complete drag function based on equation 2.48. Removing the tyre
temperature effects, driveline losses and undriven wheel losses the complete drag function is
represented by equation 6.2.
=
+ 6.2
6.3 Coefficient sensitivity analysis.
For the purposes of this investigation the sensitivity of a given coefficient is defined as the
change in overall RMS error associated with a 1 % change in the value of the coefficient. If
the sensitivity of one coefficient is high relative to the others then that coefficient will be
determined more easily by the optimisation, and will be less suseptible to noise in the
measured data. For ease of interpretation of the results the sensitivities have been normalised
using the most sensitive value.
Coefficient sensitivities can be determined by inputing steady wind conditions to the
simulator. For a range of wind speeds each coefficient is varied from its nominal value and
the resulting RMS error calculated by comparing the speed / time data calculated using the
perturbed coefficient with the speed / time data generated at its nominal value. The
sensitivities of coefficients AD, BD and CDo are virtually independent of the level of wind
input and are shown below in table 6.1.
80
ValidiJtion of analytical software
Coefficient sensitivities using simulated coastdown data
Coefficient Sensitivity (ms_I) Normalised
Sensitivity
Ao 0.03 0.43
Bo 0.012 0.17
Coo >nominal 0.04 0.57
Coo <nominal 0.07 1.00
Table 6.1
With Ko the sensitivity is highly dependent on the crosswind input. Figure 47 shows the
RMS error against Ko for crosswinds of 1,2 and 3 ms· l . The sensitivities calculated are
given below in table 6.2, the sensitivity in zero crosswind is zero. (Note: In the simulation
exercise winds have been specified in terms of a headwind and crosswind input, in practice
the sensitivity of Ko is dependent on the actual range of yaw angles generated.)
Crosswind
input (ms_I)
o 1
2
3
Sensitivity of yaw coefficient KD
Sensitivity
ofKD (ms_I)
0.0
0.0002
0.0007
0.0015
Table 6.2
Normalised
sensitivity \ (wrt. CDo<nominal)
0.003
0.01
0.02
It can be deduced from this simple check that as RMS error is relatively insensitive to the
value of Ko this coefficient will be difficult to determine in the minimisation, but as the
ambient conditions become more 'windy' Ko becomes more sensitive. One of the
requirements of this method is therefore that testing is conducted when the ambient wind is
81
Validation of analytical software
relatively high, in direct contradiction to the requirements of the standard method. Confidence
levels in the extracted coefficients are a function of the sensitivities and the overall noise, we
can therefore predict that in practical testing the highest level of confidence will be achieved
for CDo followed by AD, BD and the lowest confidence will be in KD.
In practice the error in a single coefficient will not only be exhibited as an increase in the
RMS curve fitting error, but also as small changes in the other coefficients because of the
presence of cross-sensitivities ..
6.4 Summary of the simulated data.
The constants used throughout the simulation exercise are given in tables 6.3 - 6.6 below.
Vehicle parameters.
AD 0.01
BD 2.0 E-4 (S-l)
CDo 0.4
KD 0.614
M 1100 kg
Me 1130 kg
Table 6.3
Ambient wind characteristics.
Crosswind scale length CLw".) Headwind scale length CLwh)
Dryden filter input noise bandwidth
Turbulence ratio
Table 6.4
82
30.0m
30.0m
DC-1Hz
0.4
Validation of analytical software
Anemometer dynamic characteristics.
Vane distance constant
Vane damping factor
Anemometer distance constant
Vehicle length
Table 6.5
Imposed noise levels
Measurement noise
Vehicle speed O.OS ms· l Coeffic't
Yawangle 0.01 rad
Relative airspeed O.OS ms· l Ao
Bo
Coo
Table 6.6
1.07 m
0.40
1.Sm
4.Sm
System noise
Nominal
value
0.01
2.0 E-4
0.4
Noise
1.0 E-4
1.0 E-S
S.O E-3
In table 6.7 the simulated coastdown tests are summarised. Under the headings instrument
dynamics and noise the entries are limited to Y or N indicating whether this block has been
included in the simulation. Under the heading 'model' is the type of model used, where
'basic' stands for the simplified form of equation 6.1 and 'comp' is the full model given in
equation 6.2.
83
Validation of analytical software
Summary of simulation cases.
Case Descri ption Instrument Noise Model Head Cross
dynamics M'ment System wind wind
1 validation N N N Basic 1.0 1.0 2 validation N N N Basic 2.0 2.0
3 validation N N N Basic 3.0 3.0
4 validation N N N Basic 0.0 2.0
5 validation N N N Basic 0.0 3.0
6 + spatial N N N Basic 3.0 3.0
-------------------------------------------------------------------------------------------------------------
7
8
9
IO
11
12
13
14
15
16
17
18
19
dynamics
noise
full
model
Y
Y
N
N
N
N
interp. CD('V) N
combined Y
Y
Y
Y
Y
Y
N
N
y
N
N
N
N
Y
Y
Y
Y
Y
Y
Table
84
6.7
N
N
N
Y
N
N
N
Y
Y
Y
Y
Y
Y
Basic
Basic
Basic
Basic
Comp
Comp
Basic
Comp
Comp
Comp
Comp
Comp
Comp
2.0 3.0
2.0 2.0
2.0 3.0
2.0
2.0 2.0
3.0 3.0
0.0 0.0
2.0
3.0
2.0 2.0
2.0 3.0
2.0
2.0 2.0
3.0 3.0 3.0 3.0
Validation of analytical software
6.5 Discussion of results from simulated data.
The examples outlined in section 6.4 have been analysed using program COAST which has
been developed for the analysis of real track data. Practical use of the analysis software
makes the specification of any particular analysis very simple. The operator is requested to
enter start values for the four coefficients (Ao,Bo, Coo and Ko) and is then asked to specify
which are to be treated as variables. Those parameters that are not specified as variables are
constrained at the initial estimate during the minimisation.
6.5.1 Four term analysis
The four term analysis is the most complex method applied to the data. Using this analytical
approach the three standard drag coefficients must be determined, and in addition a fourth
term Ko, to describe the variation of Co with yaw angle. Results for the 19 cases are
summarised in table 6.8. As an example of the simulated data one of the runs in the pair that
constitutes case 3 is shown in figure 48.
The validation runs 0-6) clearly show the problems involved in extracting Ko. As the level
of wind increases the estimate of Ko improves, as the range of yaw angles generated
increases. In the cases of pure crosswind, where the maximum yaw angles are encountered , (4 and 5) the estimates are very good. These validation runs represent what is in effect
'perfect' data with the only source of error being due to the rounding off when it is written to
the data file (to five decimal places as is the case when the data is recorded during real
testing). Referring back to table 6.2 it is seen that Ko is only sensitive at the third decimal
place in terms of the primary measured parameter (speed), even for the relatively high
crosswind case. The results for the remaining coefficients are not seriously affected by the
error in determining Ko, the errors in Ao and Coo are negligible in all cases, and the error in
Bo (the most insensitive term after KD) in the worse case is 0.75%.
Considering the remaining tests; the effect of including the instrument and vehicle dynamics
in the simulation is to introduce errors in all four coefficients, the errors increase with
increasing ambient wind, for a headwind and crosswind of 3.0 ms· l the errors introduced are
1% in Ao, 1.6% in BD' 0.73% in CDo and 4.7% in KD. Figure 49 shows a comparison of
the actual ambient wind characteristics, and those recorded by the anemometers. When
measurement noise is superimposed on the signals (case 10), the value of KD determined is
approximately 4 times too low, in addition there are errors of 3.8% in AD' 1.85% in BD and
85
Validation of analytical software
0.4% in Coo. The level of system noise used in case 11 does not introduce as significant
errors as the measurement noise. Using the complete mathematical model of equation 6.2 in
cases 11 and 12 the results are directly comparable with those of 2 and 3, the most significant
errors are 3.3% in Bo and 9% in Ko. The effect of the simplification using Ko to represent
the variation of Coo with yaw angle is analysed by using the Co('!') characteristic measured in
the wind tunnel to generate the coastdown data (case 13), for comparison with 2, this results
in small changes in all of the coefficients.
Case Description
No.
1 validation 2 3 4 5 6 + spatial
7 8
dynamics
9 noise 10
11 full 12 model
Results for four term analysis.
Head
wind
1.0 2.0 3.0 0.0 0.0 3.0
2.0 3.0
2.0 2.0
2.0 3.0
Cross
wind
1.0 2.0 3.0 2.0 3.0 3.0
2.0 3.0
2.0 2.0
2.0 3.0
AD
0.00999 0.00999 0.00999 0.01000 0.01000 0.00999
0.01005 0.01010
0.01038 0.01008
0.00998 0.00990
Results
BD(xlO 4)
2.000 1.998 1.985 2.000 2.000 1.986
1.989 1.968
1.963 1.973
2.003 2.066
CDo
0.4000 0.4001 0.4005 0.4000 0.4000 0.4005
0.4024 0.4029
0.4016 0.4014
0.4010 0.4007
KD
0.678 0.643 0.631 0.616 0.613 0.628
0.585 0.588
0.143 0.434
0.644 0.669
-------------------------------------------------------------------------------------------------------------13 interp. Co ('!') 2.0 2.0 0.01001 1.997 0.4005 0.654 -----.----------------------.--------------------------------------------------------------------------------14 combined 2.0 2.0 0.01016 1.960 0.4041 0.244 15 2.0 2.0 0.01010 2.090 0.3996 0.404 16 3.0 3.0 0.00981 2.103 0.3967 0.796 17 3.0 3.0 0.D10l7 1.890 0.3944 0.693 18 0.0 3.0 0.00988 2.184 0.4045 0.489 19 0.0 3.0 0.01010 2.177 0.4032 0.864 14·19 Averages 0.01009 2.064 0.4002 0.593 14·19 Std. dev. 1.5% 5.7% 1.1% 40.8%
Table 6.8
The true effect of measurement and system noise can only be analysed by considering a
number of tests. In examples 14 to 19 all blocks in the simulation are combined, and the
overall performance of the system addressed. The weighted average values are given at the
86
[- --
Validation of analytical software
bottom of table 6.8, along with the percentage standard deviations for each coefficient over
the 6 pairs of runs. These reflect the relative sensitivities of the four coefficients, the higher
the sensitivity of the coefficient the less the spread in the calculated results, the largest spread
of results therefore occurs in KD which has the lowest sensitivity.
6.5.2 Three term analysis
The most generally applied three term analysis is when it is assumed that the CD(\jI)
characteristic is known and that the coefficients AD, BD and CDo are to be determined. The
results from the analysis of the simulated cases are given in table 6.9.
Results using three term analysis (KD = 0.614)
Case Description Head Cross Results
No. wind wind AD BD (xlO4) C Do KD
1 validation 1.0 1.0 0.01000 2.000 0.4000 2 2.0 2.0 0.01000 1.997 0.4001 3 3.0 3.0 0.01001 1.982 0.4006 4 0.0 2.0 0.01000 2.000 0.4000 5 0.0 3.0 0.01000 2.000 0.4000 6 + spatial 3.0 3.0 0.01001 1.987 0.4006 ---------------------------------------.--------------------------------------------.------------------------7 dynamics 2.0 2.0 0.01004 1.992 0.4023 8 3.0 3.0 0.01005 1.975 0.4027 --------------------------------------------------.----------.----------.-----------.------------------------9 nOise 2.0 2.0 0.01011 1.985 0.4015 10 2.0 2.0 0.01000 1.979 0.4013 -----.----------------------------------------------------------------------------------------------------.--11 full 2.0 2.0 0.01000 2.002 0.4010 12 model 3.0 3.0 0.00999 2.029 0.4015 ------------------------------------------------------------------------------------.------------------------13 interp. CD(\jI) 2.0 2.0 0.01000 1.996 0.4003 --------_ .. _-------_.------------------.. --------------------------------------------------------------------14 combined 2.0 2.0 0.00998 1.975 0.4036 15 2.0 2.0 0.01001 2.085 0.3998 16 3.0 3.0 0.00987 2.091 0.3978 17 3.0 3.0 0.01003 2.009 0.3989 18 0.0 3.0 0.00997 2.046 0.4021 19 0.0 3.0 0.01004 2.062 0.3983 14-19 Averages 0.00998 2.045 0.4001 14-19 Std. dev. - 0.62 % 2.21% 0.57 %
Table 6.9
87
Validation of analytical software
This specification of the problem is useful to provide calibration data for a chassis
dynamometer. and as input data to vehicle performance and fuel economy simulation
software. as in both applications it is assumed that there is zero ambient wind.
Throughout the tests the analysis determined results that agree well with the input coefficients
.and the levels of accuracy correlate with the results from the sensitivity analysis. As in all
'constrained analysis methods it is important to consider the effect of the chosen value for the
constrained parameter. In the above results the value of Ko is 0.614 which is the input value.
In table 6.6 the effect of error in Ko is addressed; the results show that the most sensitive
term to errors in Ko is AD-
Error resulting from constraining KD
Case % Error per % error iri KD
AD BD C Do
1 0.0006 0.0 0.0
2 0.00035 0.02 0.0
3 0.074 0.06 0.01
4 0.025 0.0004 0.0
5 0.058 0.024 0.0002
Table 6.6
6.6 Anemometer calibration errors
The errors associated with anemometer calibration defects are dependent on the level of
ambient wind. although it should be noted that an error in the airspeed calibration will
introduce errors in the calculated coefficients even when there is zero wind. Errors in the
calibration of the anemometers can be assessed by introducing an error to the measured data
(before analysing to obtain the coefficients). Using the data from case 15 small scaling errors
were introduced in to the measured airspeed and yaw angle readings. and the coefficients
recalculated.
88
----------
Validation of analytical software
In the three tenn analysis a 1% error in the relative airspeed measurement resulted in a 2%
error in COo and no significant error in the remaining coefficients. For small errors in the yaw
angle calibration no significant change in the coefficients was detected. In the four tenn
analysis a I % error in the relative airspeed gave a 2% error in CDO and a 2% error in KD, but
no significant error in the remaining coefficients. A 1% error in the yaw angle calibration
generates approximately a 1 % error in Ko-
89
-- ------- -------- ----- ----- -------~~-------~~~-~--
Results and discussion - Initial study.
Chapter 7 Results and Discussion • Initial study. Page.
7.1 Introduction. 91
7.2 Practical application of coastdown and steady state methods. 91
7.3 Application of on-board anemometers. 91
7.4 Steady state results. 97
7.5 Transmission losses. 100
7.5.1 Coastdown (off-load). 101
7.5.2 Steady state (on-load). 102
7.5.3 Comparison of transmission losses. 103
7.6 Undriven wheel losses. 103
7.7 Summary of initial study. 104
90
Results and discussion -Initial study.
7.1 Introduction
The first stage of testing involved performing a series of coastdown and steady state tests to
gain experience of each method, and draw some initial conclusions. The specific objectives
of the initial study were:
i) To gain experience of the practical application of the two methods of track testing.
ii) To prove the application of on-board anemometers.
iii) To measure and compare the driveline losses in the two test modes.
iv) To measure the un-driven wheel losses in a separate laboratory exercise.
7.2 Practical application of coastdown and steady state methods.
The coastdown method is simple to perform, and is not highly dependent on driver skill.
This simplicity allows a block of coastdown tests containing a large amount of data to be
conducted quickly. In contrast the steady state test method is difficult to perform and requires
some degree of expertise from the driver to achieve close to constant speed. Covering the
speed range from 10 to 70 mph requires a minimum of 3 lengths of the test track in steady
state mode, as opposed to a single one for coastdown. The productivity of the coastdown
method is therefore substantially higher.
7.3 Application of on-board anemometers
The rationale for the use of on board anemometers has been discussed in detail in earlier
chapters, but to summarise: using conventional techniques, which do not employ on board
anemometers, correct results can only be obtained in still conditions or, if a suitable analysis
is performed, when the wind vector is in line with the vehicle and constant. There are
inherent errors in the calculated coefficients in the presence of a crosswind, or if the wind
vector is unsteady (both conditions are unavoidable in practical testing). When the local wind
vector is determined using on-board anemometers the accuracy and repeatability of the
reduced data is improved, productivity can be increased and more sophisticated analytical
techniques can be applied to extract additional information from the track tests.
For the purposes of demonstrating the importance of the continuous measurement of the
ambient wind vector two sets of coastdown data are considered. One set has been collected
. 91
'I ,
Results and discussion -Initial study.
when the wind levels were within the EEC regulation limits [21 (low wind case), and the
second set was acquired during considerably higher winds (high wind case). The wind
conditions were recorded at the proving ground control tower, as is the nonnal procedure
when conducting track tests in accordance with the EEC regulations [21. Conditions recorded
at the control tower are averaged over a 10 minute period for magnitude and direction, and
the peak level during the period is recorded. The prevailing conditions for the two sets of
coastdowns considered are shown in table 7.1, with the EEC limits included for comparison.
Wind levels during testing compared with EEC Iimits_
ECE 15.04 Table 7.2 Table 7.3
(Iow wind) (high wind)
Average (ms- l ) 3.0 1.16 4.32
Peak (ms-l) 5.0 2.13 9.02
X track peak (ms- l ) 2.0 2.0 7.3
Table 7.1
Figures 50 and 51 are examples of the raw data acquired during a single coastdown test
(excluding the measured wheel torque data). 1n the low wind case (figure 50) the airspeed is
close to the vehicle speed and the yaw angle varies about zero, which indicates the relatively
small contribution from the wind. Conversely in the case of a much higher wind level (figure
51) the airspeed is significantly lower then the vehicle speed indicating a tail-wind, and the
presence of a crosswind gives rise to large yaw angles, which increase as the vehicle speed
drops.
Six coastdowns were perfonned for each wind condition, which yield the results given in
tables 7.2 and 7.3. Each coastdown test has been analysed to generate the 3 drag coefficients
AD, BD and Coo. The RMS error for each test which has been included in the tables is a
measure of the overall 'quality of fit' of the coastdown model to that set of data, and is of a
similar magnitude from test to test. The weighted averages for the coefficients and their
respective standard errors of estimate and standard deviations are also shown. The calculation
of the weighted averages and the measures of accuracy have already been covered in detail in
92
-------
Results and discussion -Initial study.
chapter 5. These statistics are interpreted as follows; weighted average is the best estimate of
the coefficient from the group of coastdowns in a least squares sense; the standard error of
estimate is the uncertainty in the determination of the coefficient from the given set of data,
and the standard deviation is a measure of the spread of results within the group, or the test to
test variability.
Coastdown data gathered during 'Iow' wind conditions
------------- Coefficients ----.--- .... --- RMS
AD BD C Do error (ms-I)
(srn-I) 0.0098 0.369E-3 0.354 0.0297 0.0094 0.205E-3 0.418 0.0283 0.0092 0.285E-3 0.401 0.0265 0.0099 0.165E-3 0.362 0.0220 0.0093 0.194E-3 0.426 0.0235 0.0106 0.261E-3 0.362 0.0233
Weighted Standard Standard
averages error deviation
AD 0.0095 ± 3.85 E-5 (0.41 %) 5.2 E-4 (5.5%)
BD(sm- l ) 0.239 E-3 ± 4.81 E-6 (2.01 %) 7.5 E-5 (31.4%) C Do 0.386 ± 1.45 E-3 (0.38%) 0.032 (8.3%)
Table 7.2
For the low wind cases (table 7.2) the standard error of estimate of each coefficient is small,
indicating a good overall fit between the measured data and the coastdown model. The largest
error in percentage terms is attributed to the coefficient B()o which reflects its lower sensitivity
(as was demonstrated in chapter 6). The standard deviations show a similar pattern, with the
greatest spread occurring in BD. For the six tests the standard deviations in AD, BD and Coo
are 5.5%, 31.4% and 8.3% respectively. Depending on the application required for the drag
data the test engineer must decide on the acceptability of the level of confidence achieved, if it
is not sufficient then fur:ther tests must be conducted.
93
-- - - - -,---~--- - ------ - - - -
Results and discussion -Initial study.
In table 7.3 the results from the tests conducted in the higher winds are reported; the RMS
error levels are similar to those in the low wind case and consequently the standard errors of
estimate are also similar. The standard deviations have increased moderately to 6.2%.31.2%
and 9.6% for the coefficients AD. BD and Coo respectively. This increase in the spread of
results may be attributed to some element of the ambient wind correction. Steady state
anemometer errors cause only a shift in the calculated values of the coefficients so the effect
seen must be a dynamic one. This can be studied by examining the curve fit residuals for a
single coastdown conducted in high wind conditions and a single coastdown for a low wind
case. These are shown in figures 52 and 53. The magnitude of the residuals is approximately
equal for the high and low wind cases (as already demonstrated by the RMS errors) and there
is no clear trend in the residuals which would indicate that an inappropriate model is being
applied. There does however appear to be a very low frequency trend in the residuals. which
is more evident in the high wind case. To ensure that this effect is not related to the ambient
wind the residuals were correlated with the measured yaw angle and airspeed but no
correlation was found.
Coastdown data gathered in 'high' wind conditions
.. _----------- Coefficients ------------- RMS
AD BD Coo error (ms-I)
(srn-I) 0.0104 0.127E-3 0.431 0.0276 0.0091 0.380E-3 0.319 0.0277 0.0110 0.277E-3 0.403 0.0234 0.0102 0.258E-3 0.380 0.0270 0.0101 0.259E-3 0.393 0.0234 0.0106 0.238E-3 0.376 0.0283
Weighted Standard Standard
averages error deviation
AD 0.0103 4.40E-5 (0.43%) 6.4E-4 (6.2%)
Bo(sm-I) 0.260E-3 5.61E-6 (2.15%) 8.1E-5 (31.2%)
Coo 0.384 1.70E-3 (0.44%) 0.037 (9.6%)
Table 7.3
94
Results and discussion - I nidal study.
Without the continuous ambient wind measurement the basic coastdown speed time data can
still be analysed to extract values for the three coefficients. A su=ary of the results for the
data of tables 7.2 and 7.3 is given in table 7.4. These coefficients have been calculated using
the standard assumption that the ambient wind can be neglected, and only the final averaged
results have been quoted.
Effect of neglecting ambient wind correction.
Low wind case (as table 7.2)
Weighted Standard Standard
averages error deviation
AD 0.0095 ± 4.52E-5 (0.48%) 8.5E-4 (8.9%)
BD(sm·1) 0.174E-3 ± 5.85E-6 (3.36%) 1.6E-4 (91.9%)
CDO 0.419 ± I.78E-3 (0.43%) 0.043 (10.3%)
High wind case (as table 7.3)
Weighted Standard Standard
averages error deviation
AD 0.0109 7.50E-5 (0.69%) 2.6E-3 (23.9%)
BD(sm·1) 0.278E-3 9.81E-6 (3.53%) 5.7E-4 (206.5%)
CDo 0.420 2.90E-3 (0.69%) 0.16 (38.1%)
Table 7.4
In both the low and high wind examples the actual values of the coefficients have altered, but
the difference between the values calculated using the ambient wind data and those in table
7.4 do not appear to be-related to the levels of ambient wind. For the low wind case AD is
unchanged, BD is -27% and CDo is +8.5%. In the high wind case AD has increased by 5.8%,
95
Results and discussion - Initial study.
BD by 7% and Coo by 9.4%. The reason for the unpredictable nature of the errors can be
explained by considering the errors calculated for each coefficient. The standard error of
estimate has increased in all cases from those in tables 7.2 and 7.3, indicating a worse fit
between the speed time curve and the coastdown model, but the percentage errors when the
ambient wind is neglected are still relatively small. This result is because the combination of
the coastdown function and the least squares method used in the curve fitting has allowed the
values of the coefficients to be traded off against each other in order to achieve the minimum
error.
This effect can be confirmed by an examination of the standard deviations (or test to test
spread) of the coefficients. In the low wind case the errors introduced by neglecting the
ambient wind should be relatively small. The standard deviations of Ao and Coo have
moderately increased from 5.5 and 8.3% respectively to 8.9 and 10.3% respectively, but the
standard deviation in Bo, the least sensitive coefficient, has approximately tripled from
31.4% to 91.9%. In the high wind example the errors introduced by the ambient wind are
more significant, so that the minimum curve fit error cannot be achieved by simply trading
off the least sensitive coefficient. The standard deviations in AD and Coo have therefore
increased dramatically by a factor of four, and the standard deviation of Bo has increased by
a factor of approximately six. The confidence in these results is therefore very low.
Results of coastdown tests reported in the literature do not in general provide a detailed
analysis of the errors associated with the calculated results, Emtage [5] does report full sets of
coastdown results, from a non-anemometer method. The results for two sets of six
coastdowns are summarised in table 7.5 below, both sets were obtained when the ambient
wind was within the prescribed EEC limits [2].
The analysis used in the work by Emtage [5] attempts to take account of the ambient wind by
measuring the mean wind speed and direction during the test and including it in the analysis.
The results demonstrate that a continuous measurement of ambient wind is essential to
produce reliable results.
96
Results and discussion -Initial study.
Summary of non-anemometer results reported by Emtage,
(reference 5).
Weighted
averages
0.0108
0.494E-3
0.324
Set 1
Set 2
0.0095
0.504E-3
0.310
Table 7.5
Standard
deviation
1.49E-3 (13.7%)
1.80E-4 (36.3%)
0.055 (17.0%)
1.91E-3 (20.1 %)
2.79E-4 (55.4%)
0.086 (27.7%)
It is evident from these results that without the use of on-board anemometers the thtee
coefficients cannot be determined with a reasonable level of certainty, even in wind
conditions that are within the prescribed EEC limits [21. When testing must be conducted
without anemometers it is recommended that a two term analysis is used which determines
only AD and COo.
7.4 Steady state results
In the initial study five sets of steady state data were acquired, with each set consisting of a
total of twelve steady speed runs, with data gathered in both directions on the track at six
steady speeds. Uncorrected steady-state data are shown in Figure 54. At each speed the data
have been averaged for clarity, and error bars representing ± 1 standard deviation of the
measured total wheel force (sum of left and right wheels divided by dynamic tyre radius) are
included to show the spread of the raw data. The two distinct sets of data which appear on
97
-._--- ~- - --------- --- --------
Results and discussion - Initial study.
the graph are the tests in opposite directions on the track. The differences are primarily due to
the ambient wind as the track has nominally zero gradient After performing the correction as
described in section 5.4.1 the data is fitted with a quadratic function to detennine the three
coefficients. The data presented in figure 54 is shown in its corrected form in Figure 55; also
showing the least squares quadratic fit
Results from the five sets of steady-state tests are shown in Table 7.6 with the prevailing
wind conditions obtained from the proving ground system.
Steady state test results
......... _ ....... _- Coefficients ...... __ ....... _- ------ Wind (rns-I )
AD BD Coo Mean Peak X track
(srn-I) peak
0.0121 -.280E-4 0.462 2.6 4.9 2.7
0.0106 . 195E-4 0.419 3.7 7.2 4.2
0.0111 .292E-4 0.380 5.1 9.2 7.2
0.0098 .600E-3 0.329 2.3 5.2 3.2
0.0111 .36IE-3 0.355 1.3 2.3 1.7
Weighted Standard Standard
averages error deviation
AD 0.0110 1.85E-4 (1.68%) 8.38E-4 (7.6%)
BD (srn-I) 0.208E-3 2.20E-5 (10.57%) 2.74E-4 (131.7%)
Coo 0.410 5.37E-3 (1.31 %) 0.053 (12.9%)
Table 7.6
The data shown has been collected over a range of wind conditions, varying from within the
EEC limits [2] to levels similar to those previously quoted for the high wind level coastdown
case (table 7.3). The total amount of data acquired for the five steady state sets is
approximately equal to 14 coastdowns.
98
Results and discussion -Initial study.
The standard errors of estimate are significantly higher than in the coastdown case, showing
a worse fit to the mathematical model than for coastdown data. It is suggested that this is due
to a higher level of noise on the raw data. This is confirmed by examining a plot of the
residuals (figure 56), shown as error bars of ±1 standard deviation, (normalised with respect
to the steady speed drag force at the maximum speed tested, because the curve fit is in terms
of drag force as opposed to speed in the coastdown) and comparing it with figures 52 and
53. The normalised residuals in steady state are an order of magnitude greater than in
coastdown. The standard deviations also reflect the lower levels of accuracy achieved in
steady state particularly the BD term which has a standard deviation of 131.7%.
When on-board anemometry is not available the usual method for analysing steady-state
torque data is to average runs in opposite directions on the track. An example set of data is
shown in Figure 57. At first inspection the graph appears to give encouraging results, but the
errors associated with ignoring the time varying winds become evident when the coefficients
are extracted from the data. Overall results for the same five sets of data as above are given
below in table 7.7.
Steady state results for averaged data
Weighted
averages
AD 0.0162
BD(sm·1) -0.433E-3
C Do 0.524
Standard
error
4.70E-4 (34.5%)
5.S0E-4 (127.0%)
0.013 (2.48%)
Table ,.,
99
Standard
deviation
3.7E-3 (22.8%)
9.0E-4 (208%)
0.13 (24.8)
Results and discussion - Initial study.
Using this method it is clearly difficult to estimate the three basic terms of the drag function.
Suggesting that a two term drag function to determine only AD and Coo may provide more
useful results. In much of the steady state work reported in the literature the BD term is
ignored [111.
7 _ 5 Transmission losses
The transmission losses have been measured during each coastdown using the wheel torque
meters and included in the coastdown optimisation analysis so that the coefficients AD, BD
and Coo can be compared with those calculat~ from steady state data (steady state results do
not include the driveline losses because the drag is measured at the wheels).
In general, during coastdown testing, the driveline losses are ignored [5,61, in which case
their effect is distributed throughout the main coefficients giving misleading results. This
accounts for the exceptionally low values of Coo and high values of BD reported in table 7.5
(after Emtage [51), which are for a similar vehicle to that used in this research. If the driveline
drag is included then it is nonnally measured during separate tests in a laboratory [Ill. The
usual method is to perfonn a coastdown on the driveline only, as described for the un-driven
wheel losses in section 5.6. However the losses are dependent on the drive line oil
temperature [261 so this must also be measured during both the coastdowns on the track, and
during the laboratory tests. By performing the driveline coastdowns over the range of oil
temperatures encountered on the test track a regression can be performed to determine a
suitable function for calculating the driveline losses during a specific track coastdown. The
usual form used to represent the driveline losses is a linear function with speed, with a linear
correction for oil temperature [Ill.
Although it was unnecessary for the purposes of the coastdown analysis to mathematically
model the driveline losses, as a subsidiary exercise each set of driveline data was fitted with a
linear function of the form described in section 2.3.2 to determine the coefficients At and Bt'
To allow a comparison of the coastdown losses with the steady state driveline losses an
additional torque transducer was fitted to the input shaft of the gearbox, as described in
section 3.3, so that the steady state transmission losses could also be calculated by
subtracting the total torque at the driven wheels from the input torque to the gearbox.
100
Results and discussion -Initial study.
7.5.1 Coastdown (offload)
The results for the two sets of coastdown data previously reported are shown in table 7.8.
Driveline losses in coast down.
(Iow wind case)
Coefficient Standard error
AI BI At B t (N) (Nsm- i ) (N) (Nsm- i )
19.53 1.38 0.29 0.017 14.57 1.51 0.20 0.012 18.21 1.62 0.24 0.014 19.31 1.67 0.24 0.014 16.44 1.72 0.24 0.015 15.01 1.72 0.29 0.018
Weighted Standard Standard average error deviation
At(N) 17.03 0.10 (0.59%) 2.1502.6%) BI (Nsm- i ) 1.59 6.4E-3 (0.40%) 0.13 (8.2%)
(high wind case)
Coefficient Standard error
At Bt AI BI (N) (Nsm- i ) (N) (Nsm- i )
8.85 1.49 0.39 0.023 12.47 1.52 0.30 0.017 9.78 1.52 0.26 0.017 2.84 1.64 0.29 0.017 -3.66 1.62 0.23 0.014 4.33 1.36 0.33 0.019
Weighted Standard Standard average error deviation
-- - .
At (N) 5.77 0.18 (3.5%) 5.83001%) BI (Nsm- i ) 1.53 6.3E-3 (0.41%) 0.10 (6.5%)
Table 7.8
101
Results and discussion -Initial study.
Comparing the driveline coefficients At and Bt with the main coefficients AD and BD show
that the average driveline constant term (11 N) is approximately 10% of the constant tyre
loss, and Bt has approximately the same magnitude as the tyre velocity dependent term. It is
therefore essential that the driveline losses are removed from the coastdown analysis if a
comparison between coastdown and steady state results is to be made, and if the sources of
drag in coastdown are to be accurately separated. An example of the driveline data from the
wheel torque meters is given in figure 58.
Examining in detail the results in table 7.8 an important result is established. The velocity
dependent coefficient is consistent from test to test and consistent between the low wind case
and the high wind case. However the constant term is repeatable only in the low wind
examples. The standard deviation of the constant term during the high wind case has a similar
magnitude as the standard deviation of AD in the main coastdown analysis (from table 7.3 the
standard deviation in AD is 6.4E-4, which is equal to 7 N at the reference mass of the
vehicle). Examination of the wheel torque meters revealed that during testing wear had
occurred on the splined portion due to the large torque reversals encountered during normal
driving, this had resulted in instability of the torque meter zero. The data used in the high
wind case was acquired at the end of the initial study, when the problem was the most
significant. Before conducting the main coastdown tests a new set of wheel torque meters
were designed with a closer tolerance spline; these were also made more sensitive to improve
the driveline loss measurements.
7.5.2 Steady state (on load)
Figure 59 shows the total drag characteristic measured at the wheels and at the gearbox input
shaft. For clarity the data has been averaged at each data point. The difference between the
drag measured at the wheels and that measured at the input to the gearbox is the driveline
loss. To allow a simple comparison of the driveline loss levels in coastdown and in steady
state the coefficients At and Bt have been calculated. Results for the five sets of coastdown
data presented in previous sections are given in table 7.9. An example of the data is shown
in figure 60, the data has been averaged at each speed, and the error bars have been included
to show the spread of the data.
102
Results and discussion -Initial study.
Steady state driveline losses
Coefficient
At B t (N) (Nsm-l) 40.6 0.13 42.4 -0.64 34.2 -0.67 31.2 0.68 71.3 -1.79
Weighted
average
At (N) 36.3
Bt (Nsm-1) 0.0
Standard error
At B t (N) (Nsm-1)
13.1 0.63 4.2 0.20 5.6 0.26 3.1 0.15 13.1 0.64
Standard Standard
deviation error
2.2
0.11
Table 7.9
16.0
0.93
7.5.3 Comparison of transmission losses
Due to the difficulties of measuring the driveline losses during steady state, and the unreliable
results for the high wind case in coastdown, it is difficult to draw any finn conclusions on
the differences between coastdown and steady state driveline losses. However, comparing
the results in table 7.9 with the results for the low wind case in table 7.8 it appears that the
constant friction tenn is approximately double the coastdown value in steady state mode,
reflecting the higher levels of torque being transmitted. The velocity dependent tenn is zero in
steady state.
7.6 Undriven wheel losses
Undriven wheel losses were detennined using the method described in section 5.6. An
example of the data from a test on a single wheel is given in figure 61. Three tests were
103
Results and discussion - Initial study.
conducted on each wheel, giving the results shown in table 7.10. It is evident that the
contribution from the un-driven wheels is small accounting for only 8.4 N at 50 mph. The
results obtained in the initial study were used throughout the main study.
Un driven wheel losses
Test Nearside Offside
No. AUD BUD Auo Buo
1 1.76 0.117 1.57 0.109
2 1.58 0.123 1.58 0.115
3 1.55 0.125 1.58 0.121
mean 1.66 0.121 1.58 0.114
Total std. dev.
Au (N) 3.24 0.155 (4.8%)
Bu (Nsm·1) 0.232 0.012 (5.1%)
Table 7.10
7.7 Summary of the initial study
The analytical procedures described in earlier chapters and used in the analysis of the data
presented in this chapter have been designed to eliminate the differences between results
obtained in coastdown and steady state tests. Coefficients obtained in the two test modes may
therefore be directly compared. Table 7.11 summarises the results for the main coefficients
presented in this chapter, and in addition includes results for the complete set of 24
coastdowns which were performed in the initial study.
The road load coefficients determined from steady state tests correlate well with those from
coastdown. The constant term AD is approximately 10% higher in steady state, the speed
dependent term BD is approximately 12% lower and the aerodynamic term is 4.5% higher in
104
Results and discussion - Initial study.
steady state. Calculating the total drag at 50 mph reveals that the total drag is 4.5% higher in
steady state, which may be attributed to the increase in tyre losses as the tyre transmits torque
(see section 2.3.1.6).
Comparison of the aerodynamic coefficient with the wind tunnel derived value also shows
good correlation; in both test modes agreement is within 2.5% of the tunnel measured value.
Summary of initial study results
------------- Coastdown ------------- Steady Wind
state tunnel
Low wind High wind Set of 24
AD 0.0094 0.0103 0.0098 0.0110
Std.dev 5.5% 6.2% 4.9% 7.6%
BD 0.23IE-3 0.260E-3 0.233E-3 0.208E-3
Std.dev 31.4% 31.2% 27.3% 131.7%
C Do 0.386 0.384 0.391 0.410 0.401
Std.dev 8.3% 9.6% 6.4% 12.9%
Table 7.11
General comments on the conduct of the two tests has already been made in the introduction
(7.1) which suggests that the coastdown test is preferable in practical terms. It is also clear
from the results so far presented that the accuracy and repeatability of the coastdown test is
greater. In view of both of these conclusions the main study concentrates on the development
of the coastdown method as an advanced means of determining road load data.
105
--------- ----
Results and discussion· An advanced coastdown metluJd.
Chapter 8 Results and discussion • An advanced coastdown method.
Page.
8.1 Introduction 107
8.2 Assessment of results using the three term analysis 108
8.3 Constrained analysis. 114
8.4 Development of a four term analysis. 117
8.5 Driveline losses in coastdown. 121
8.6 Summary of the results. 123
106
Results and discussion - An advanced coastdown method.
8.1 Introduction
It has been demonstrated in chapter 7 that the most accurate and repeatable road load data is
obtained from coastdown tests using on-board anemometers. This chapter concentrates on
the further development of the practical and analytical methods applicable to the coastdown
test, and assesses the overall accuracy of the technique.
Before any additional testing was undertaken a second set of wheel torque meters were
purchased which had a closer tolerance spJine attachment and had only two thirds of the total
range of the original pair. This would provide a more accurate and repeatable measurement of
the off load driveline losses. In addition a modification to the test procedure was introduced
to ensure that the instrumentation was performing correctly. The revised coastdown test
method is as follows.
i) Cold tyre pressure is set according to the manufacturers instructions, and the
front disc pads released to eliminate unpredictable parasitic drag.
ii) The vehicle is weighed on the MIRA weigh-bridge in its test configuration
and the mileage trip set to zero.
iii) Vehicle conditioning is c'arried out at a constant 50 mph for 30 minutes.
iv) With the vehicle stationary on the track all instrumentation is appropriately
zeroed, and a 10 second calibration file obtained.
v) A pair of coastdowns is conducted.
vi) A 10 second calibration file is recorded with the vehicle stationary on the
track, and the mileage trip reading recorded.
vii) Steps v and vi are repeated until all the required test data have been collected
viii) The vehicle is weighed a second time and the mileage trip reading recorded.
The calibration files were acquired as a check on the zero stability of the readings, particularly
the wheel torque meters. Prior to analysing the coastdown data the calibration files were used
to correct any drift which may have occurred. In general any corrections were very small, but
a number of sets of data were discarded because of recurrent problems with the wheel torque
meters. The availability of accurate, non intrusive, low range wheel torque meters would be
an advantage in track drag measurements.
107
Results and discussion - An advanced coastdown method.
8.2 Assessment of the results using the three term analysis
An example block of six coastdowns is shown in table 8.1. The RMS curve fitting errors for
the individual tests and the standard error of estimate of the coefficients are similar in
magnitude to those found in the initial study (ie. tables 7.2 and 7.3). However the standard
deviations of the coefficients Ao and Coo have been significantly reduced, and a small
reduction in the absolute standard deviation of Bo has been achieved.
Example set of six coast downs
------------- Coefficients ------------- RMS
AD BD C Do error (ms-I)
(srn-I)
0.0099 0.234 E-3 0.393 0.0257
0.0100 0.229 E-3 0.378 0.0354
0.0102 0.194 E-3 0.410 0.0277
0.0105 0.803 E-4 0.438 0.0198
0.0097 0.204 E-3 0.408 0.0201
0.0102 0.108 E-3 0.419 0.0284
Weighted Standard Standard
averages error deviation
AD 0.0101 ± 4.00 E-5 (0.39%) 3.1 E-4 (3.1 %)
BD(sm-I) 0.166 E-3 ± 4.90 E-6 (2.95%) 6.5 E-5 (39.0%) C Do 0.406 ± 1.61 E-3 (0.39%) 0.021 (5.2%)
Table 8.1
It was suggested in section 7.5.1 that a large proportion of the variability in the main
coefficients could be attributed to inaccurate wheel torque meter data. An examination of the
transmission loss coefficients determined during the coastdowns reponed in table 8.1 (Table
8.2) reveal that a significant improvement in the standard error of estimate and the
repeatability of both coefficients has been achieved. If the standard deviation of Ao is
108
Results and discussion - An advanced coastdown metlwd.
converted to Newtons it can be seen that the improvement in accuracy of the coefficient AD is
approximately equal to the improvement in accuracy of At. The general improvement in the
accuracy of the results can therefore be attributed to the improved test method and the
increased accuracy of the wheel torque meters.
Driveline losses for the six coastdowns in table 8.1.
Coefficient Standard error
At B t At Ht
(N) (Nsm-1) (N) (Nsm-1)
22.4 1.328 0.131 0.77 E-2
22.6 1.384 0.146 0.85 E-2
21.7 1.351 0.140 0.77 E-2
23.2 1.396 0.185 0.11 E-l
24.7 1.470 0.113 0.67 E-2
26.2 1.466 0.158 0.95 E-2
Weighted Standard Standard
average error deviation
At (N) 23.5 0.059 1.68
Bt (Nsm- i ) 1.399 3.48 E-3 0.058
Table 8.2
Results for a set of 36 coastdowns are given in !able 8.3. Each result represents the weighted
average of a pair of coastdowns conducted in opposite directions on the track. This is the
favoured method of presen!ation because it accords well with normal practice in coastdown
testing, and reduces the quantity of data to be considered. The results have also been
separated into sets of three which were conducted as a block.
109
Results and discussion - An advanced coastdown method.
Paired coastdown results using three term analysis.
0.0099 0.0105 0.0098
0.0096 0.0096 0.0098
0.0095 0.0092 0.0094
0.0095 0.0091 0.0093
0.0088 0.0093 0.0102
0.0091 0.0096 0.0093
AD BD(sm- l )
C Do
Coefficients
BD (sm- l )
0.24OE-3 0.861 E-4 0.167 E-3
0.207 E-3 0.188 E-3 0.191 E-3
0.247 E-3 0.219 E-3 0.257 E-3
0.209 E-3 0.225 E-3 0.238 E-3
0.290 E-3 0.265 E-3 0.159 E-3
0.291 E-3 0.207 E-3 0.214 E-3
Weighted
average
0.0095
0.214 E-3
0.393
Total drag @
50 mph (N) 436
0.389 0.434 0.410
0.394 0.404 0.400
0.383 0.390 0.375
0.393 0.386 0.384
0.363 0.374 0.412
0.364 0.393 0.392
Standard
error
0.16 E-4 (0.17%)
0.20 E-5 (0.93%)
0.60 E-3 (0.15%)
0.003 (0.0%)
Table 8.3
110
Total drag @
50 mph (N)
440 436 439
436 437 437
439 436 434
437 436 437
433 436 436
435 435 435
Standard
deviation
0.411 E-3 (4.3%)
0.494E-4 (23.1%)
0.017 (4.3%)
1.75 (0.40%)
Results and discussion - An advanced coastdown method.
The levels of accuracy achieved are considerably lower than those from the simulated data in
chapter 6. It is suggested that this arises from a number of sources. The principal one is that
sources of noise are much greater than that anticipated in the simulation, the additional
sources may be attributed to track surface irregularities, air turbulence effects, variation of
temperatures throughout the coastdown, vehicle attitude changes from test to test, the
inclusion of noise in the wheel torque meter data, and others. The relative accuracies of the
coefficients from the simulation agree well with those determined in practice.
Having performed and analysed a number of coastdowns it would be useful to have a better
understanding of the statistical accuracy of the results, and to attempt to quantify the accuracy
that could be expected from specific numbers of tests. The confidence limits for each of the
coefficients in table 8.3 can be determined from the standard deviations using equation 8.1.
Confidence interval = t s
-In 8.1
Where t is the relevant value from the t distribution for a given level of confidence, obtained
, from stati~tical tabl~s. Tile confidence limits at the 95% and 99% confidence levels are given
i in tabl~. 8.4, and are also expressed as a percentage of ,the m~ value for the coefficient.
Confidence intervals· Three term analysis.
Total drag @
50 mph (N)
95% level
2.04 E-4 (2.15%)
2.46 E-5 (11.5%)
8.46 E-3 (2.15%)
0.87 (0.2%)
Table 8.4
111
99% level
2.81 E-4 (3.0%)
3.38 E-5 (15.8%)
0.0116 (3.0%)
1.2 (0.27%)
------.---- ----- ---- -- --- ---- --
Results and discussion - An advanced coastdown method.
The confidence interval is a measure of how close the sample mean is to the population mean.
The coefficients AD, BD and Coo are within 2.15%,11.5% and 2.15% of the population
mean respectively at the 95% confidence level.
The fourth parameter in the table is the total drag at 50 mph, which has been included for
comparison with the EEC regulations [2]. In this regulation the statistical accuracy required
for the single parameter calculated (the actual parameter used depends on the type of test) is
a confidence interval of ±2.0% of the mean at the 95% confidence level. Using the
sophisticated coastdown technique described here the statistical accuracy of the total drag at
50 mph is ±D.2% at the 95% confidence level, or 436 ±D.87 N.
Confidence limits for the actual data gathered in this experiment are useful, but in general a
method is required for predicting the number of tests which must be conducted to achieve a
particular level of accuracy. In making these predictions it is assumed that in tests on another
vehicle under different test conditions the same coefficient of variation would result (standard
deviation divided by mean). The most suitable method in this case is to predict the percentage
confidence intervals which relate to set numbers of tests.
The confidence in the mean has already been established in table 8.4. To determine the
confidence in the standard deviation the chi squared (X2) test can be applied to infer the
population standard deviation (cr) from the sample standard deviation (s), within given
confidence limits.
2 X -
2 'l)S
2 cr
82
Using the 95% and 5% probability values for the reduced chi square (X2/'1l) the range of
values of the standard deviations for the three coefficients and the total drag are given in table
8.5. The population standard deviation has a probability of 0.05 of being less than the lower
limit in the table and a 0.95 probability of being less than the upper limit.
112
Results and discussion - An advanced coastdown method.
Population standard deviations calculated using x.2.
5% 95%
AD 0.323 E-3 <cr< 0.576 E-3
BD (srn-I) 0.388 E-4 <cr< 0.692 E-4 C Do 0.013 < cr < 0.024
Total @
50 mph (N) 1.37 < cr < 2.45
Table 8.5
The worse case occurs when the population standard deviation takes the upper value from
table 8.5, however it is assumed that it takes the most probable value, ie. that the mean and
standard deviations of the coefficients in table 8.3 are the population values. Also assuming
that the coefficients are normally distributed, the confidence intervals for a given number of
tests can be calculated using normal probability integral tables. The confidence level for n
tests is calculated using equation 8.2.
Confidence interval zs
8.2 =
The parameter z (dimensionless deviation) is determined from the tables. At the 95%
confidence level z = 1.96, hence the confidence intervals in percentage terms for different
numbers of tests are given in table 8.6.
To determine coefficients AD and CDo to within I % and BD to within 5% at the 95%
confidence level over 80 tests are required. The total drag force at 50 mph can be determined
to within I % with 95% confidence from a single test.
113
Results and discussion - An advanced coastdown method.
Confidence intervals (% ) at the 95 % confidence level
against number of tests· 3 term analysis.
Number AD BD CDo Total drag@
of tests 50 mph (N)
1 8.5 45.3 8.5 0.79 2 6.0 32.0 6.0 0.56 3 4.9 26.1 4.9 0.45 4 4.2 22.6 4.2 0.39 5 3.8 20.2 3.8 0.35 6 3.5 18.5 3.5 0.32 12 2.4 13.1 2.4 0.22 24 1.7 9.2 1.7 0.16 48 1.2 6.5 1.2 0.11 96 0.9 4.6 0.9 0.08
Table 8.6
8.3 Constrained analysis.
Using the three tenn analysis the vehicle drag can be measured and separated into its
contributions, but as a large number of tests are required to achieve a high level of confidence
in the coefficients it may be impractical in some investigations where only basic information
is required. The need for this flexibility in the method which will allow the operator to tailor
the analysis to a particular application has been highlighted throughout this work.
The simplest fonn for the results has alteady been discussed in the previous section. If only
the total load at a given speed is required then only a single pair of coastdowns will be
necessary to achieve 1 % accuracy with 95% confidence. In this case the three tenn analysis is
still required and the total load is calculated from the resulting coefficients. This technique can
be used, for example, in the calibration of a water brake dynamometer, or as a quick method
of comparing different vehicle setups.
A more complex situation, which was used as an illustration in chapter 1, is the comparison
of two or more sets of tyres (although equally it may be the comparison of different types of
aerodynamic device). Tyre losses are represented by the coefficients AD and BD' and as only
114
Results and discussion - An advanced coastdown method.
the tyres change from test to test the aerodynamic drag may reasonably be assumed to be
constant so it may be fIXed at some nominal value to reduce the optimisation to a two tenn
analysis. Using this facility Coo was constrained to the value 0.39, the results from the
optimisation are shown in table 8.7.
AD BD
0.0099 0.0097 0.0095
0.0096 0.0095 0.0096
0.0095 0.0093 0.0097
0.0094 0.0095 0.0095
0.0099 0.0094 0.0100
0.0097 0.0096 0.0094
(srn· l )
Tyre loss 50 mph (N)
Two term analysis CDo = 0.39
BD (srn-I)
Tyre loss @
50rnph
0.235 E-3 0.247E-3 0.247E-3
0.251 E-3 0.236E-3 0.242E-3
0.243E-3 0.228 E-3 0.250 E-3
0.221 E-3 0.237E-3 0.249E-3
0.254E-3 0.246E-3 0.234E-3
0.241 E-3 0.239E-3 0.228E-3
Weighted Standard
average error
167 168 166
168 165 166
165 163 167
162 163 166
169 164 168
167 165 163
0.0095 0.355 E-5 (0.04%)
0.239 E-3 0.487 E-6 (0.20%)
166 0.003 (0.002%)
Table 8.7
115
Standard
deviation
0.187 E-3 (1.97%)
0.900 E-5 (3.77%)
2.06 (1.24%)
Results and discussion - An advanced coastdown method.
It is imponant to remember that when using a constrained analysis the actual values of the
coefficients depend on the choice of the values of the constraints; in this case it depended on
the value of Coo chosen. Therefore the results can only be used for comparative purposes.
Number
of tests
1 2 3 4 5 6 12 24 48 96
Confidence intervals (%) at the 95 % confidence level
against number of tests - Tyre losses only.
----------- 2 term analysis ----------- 3 term analysis
AD BD Tyredrag@ Tyredrag@
50mph (N) 50 mph (N)
3.8 7.4 2.4 8.0 2.7 5.2 1.7 5.6 2.2 4.3 1.4 4.6 1.9 3.7 1.2 4.0 1.7 3.3 1.1 3.6 1.6 3.0 1.0 3.3 1.1 2.1 0.70 2.3 0.78 1.5 0.50 1.6 0.55 1.1 0.35 1.2 0.39 0.75 0.25 0.81
Table 8.8
If the operator is not interested in the relative magnitudes of, or changes to the coefficients
then it will be sufficient to detennine the total tyre drag at a chosen speed. In table 8.7 the tyre
drag at 50 mph is shown, and in table 8.8 there are the corresponding confidence intervals
against number of tests. The number of tests required to determine the tyre drag within 1 % is
now only 6 (note: To determine the tyre loss with a confidence limit of 1% requires the
resolution of forces 3 times smaller than for the total drag). For comparison the equivalent
tyre loss data calculated from the three term analysis is shown, in which case 64 tests are
required.
The advantages in productivity of this flexible approach to the analysis are clear from these
results, however it must be remembered that if a constrained analysis is used then the results
can only be used in a comparative exercise.
116
Results and discussion - An advanced coastdown metlwd.
8.4 Development of a four term analysis.
The methods discussed so far have demonstrated the type of accurate and flexible test system
which can be developed using on-board anemometers and a suitable analytical method. The
main drawback in the technique, however, is the continued dependence on the initial wind
tunnel tests. Two issues are involved in attempting to develop a method which does not
require the wind mnnel tests. The correct calibration of the yaw angle sensor cannot be
conducted at the test track, and the parameter Ko must be known as it is used as input to the
optimisation.
The second of these problems can be resolved by including Ko in the analysis as a control
variable instead of as an input constant. Results from the simulation exercise in chapter 6
demonstrated that Ko is insensitive compared to the other terms, and that its sensitivity
depends on the prevailing ambient wind conditions, in particular the range of yaw angles
developed during the test. The crosswinds applied in the simulation are equivalent to mean
absolute yaw angles throughout a pair of coastdowns of approximately 4.5°,9.4° and 14.8°.
The 18 pairs of coastdowns already reported have been reanalysed using the additional fourth
term Ko, and the results are shown in table 8.9, included in the table is the mean yaw angle
developed during the test.
The overall values of the three coefficients Ao , Bo and Coo are virtually unchanged from
those determined using the three tenn analysis, despite a wide variation in the calculated value
of Ko. This indicates that although it is not possible to get an accurate estimate of this fourth
term in low wind conditions, it may still be included in the analysis as it does not affect the
remaining results. The standard error of estimate of each coefficient has increased because of
the additional tenn in the analysis, but the standard deviations have been reduced so that less
tests will be required to achieve a particular level of accuracy. Using the statistical methods
described earlier in this chapter the confidence intervals against number of tests have been
calculated for the four term analysis, these are shown in table 8.10. The Ko term has not
been included because it is not practical to determine it from this data.
117
---~-----~------~------~----~--------
Results and discussion - An advanced coastdown method.
Paired coastdown results using four term analysis
---------•• ----- Coefficients --------••• -----
AD BD C Do KD Total (srn-I) (rad-Z) @ 50 mph
Mean absolute
yaw angle n 0.0098 0.0101 0.0095
0.0095 0.0094 0.0097
0.0096 0.0092 0.0094
0.237 E-3 0.177 E-3 0.183 E-3
0.223 E-3 0.189 E-3 0.176 E-3
0.253 E-3 0.196 E-3 0.225 E-3
0.393 0.393 0.404
0.380 0.400 0.407
0.377 0.396 0.388
0.0095 0.0091 0.0095
0.180 E-3. 0.406 0.215 E-3 0.391 0.199 E-3 0.399
0.0088 0.0092 0.0098
0.0091 0.0094 0.0093
AD
0.272 E-3 0.261 E-3 0.197 E-3
0.274 E-3 0.246 E-3 0.211 E-3
BD(sm-I) CDo
KD Total @
50 mph
0.367 0.376 0.399
0.369 0.380 0.394
Weighted
average
0.0094
0.217E-3
0.390
1.72
436
0.418 1.325 2.514
0.396 1.763 1.412
-0.316 0.367 3.798
0.150 0.942 3.171
2.860 1.782 3.153
2.871 2.586 0.087
440 433 439
434 435 437
439 435 434
437 436 437
432 436 435
435 435 435
Standard
error
0.19 E-4 (0.20%)
0.26 E-5 (1.2%)
0.91 E-3 (0.23%)
0.109 (6.3%)
0.003 (0.0%)
2.9 2.6 2.4
2.7 2.8 3.1
2.1 2.5 2.0
2.0 2.0 2.0
1.7 2.0 2.1
1.8 1.5 1.5
Standard
deviation
0.305 E-3 (3.2%)
0.330 E-4 (15.2%)
0.012 (3.1 %)
1.277 (74%)
2.10 (0.48%)
Table 8.9
118
-- -- ------------
Results and discussion - An advanced coastdown method.
Confidence intervals (% ) at the 95 % confidence level
against number of tests - 4 term analysis.
Number AD BD Coo Total drag@
of tests 50mph (N)
1 6.4 29.8 6.0 0.94 2 4.5 21.1 4.3 0.67 3 3.7 17.2 3.5 0.56 4 3.2 14.9 3.0 0.47 5 2.8 13.3 2.7 0.42 6 2.6 12.2 2.5 0.39 12 1.8 8.6 1.7 0.27 24 1.3 6.1 1.2 0.19 48 0.92 4.3 0.87 0.14 96 0.65 3.0 0.62 0.10
Table 8.10
The number of tests required to detennine AD and CDo to within 1 % and BD to within 5% has
reduced from over 80 to approximately 40. Assuming that in the presence of much higher
winds the KD term could be extracted from the data, the four term analysis can replace the
three term method. All the tests in the main study were conducted in low winds because this
was a requirement of the sponsor. The only data available to test the four term analysis
further is that acquired during the initial study, using the less accurate wheel torque meters.
Nine pairs of coastdowns conducted in higher winds have been analysed and the results are
presented in table 8.11.
119
Results and discussion - An advanced coastdown method.
Four term analysis for windy conditions
-------------••• ----- Coefficients ---------------------
Ao Bo CDo KD
0.0106 0.0097 0.0103
0.0103 0.Q115 0.0093
0.0097 0.0092 0.0096
Ao
(srn-I) (rad-2)
0.133 E-3 0.309 E-3 0.253 E-3
0.237 E-3 0.198 E-3 0.279 E-3
0.181 E-3 0.234 E-3 0.215 E-3
0.432 0.348 0.376
0.376 0.383 0.359
0.383 0.361 0.367
0.503 0.892 1.152
1.113 1.218 1.226
0.922 1.956 0.426
Weighted Standard
average error
0.0100 0.31 E-4
Bo (srn-I) 0.221 E-3 0.38 E-5
Coo 0.378 0.11 E-2
Ko 0.977 0.029
Table 8.11
Mean absolute
yaw angle n 4.8 5.4 5.3
5.0 3.1 4.3
5.1 2.9 5.1
Standard
deviation
0.129 E-3
0.527 E-4
0.024
0.451
The spread of results for Ko has been reduced by a factor of three while the mean yaw angle
for each test has approximately doubled. The value determined for Ko of 0.977 is
approximately 60% higher than the value calculated from the wind tunnel data . The complete
Co ('!') characteristics calculated using the optimised values of Ko from tables 8.9 and 8.11
are plotted in figure 62 and compared with that measured in the wind tunnel. In each case the
data is plotted over the yaw angle range encountered during the testing. To separate out the
Ko term the data are also shown in figure 63 with Coo removed, which shows a reasonable
fit to the wind tunnel data. In terms of yaw angle the error between the track data and that
from the wind tunnel is small, representing in the worse case an error of approximately 40,
any error in the yaw angle calibration will therefore lead to significant errors in the calculated
value of Ko. The variation in the yaw and airspeed calibrations, shown in section 4.7.2 may
120
Results and discussion - An advanced coastdown method.
account for much of this error. Additional work on the accurate calibration of the vane
anemometer is therefore required. The results demonstrate the possibilities of the four term
analysis, but funher data gathered in relatively high winds is required to test and develop the
method funher.
The calibration of the anemometers is one that extends beyond the need to eliminate the wind
tunnel tests. The results from the four term analysis of real and simulated data demonstrate
that the accurate calibration of the anemometers is essential if the complete CD ('I')
characteristic is to be determined. The simple linear corrections used in this work may
therefore be inadequate. A method for calibrating the zero yaw angle airspeed has been
developed (section 4.7.3) and was used as the basis for the airspeed calibration, but the yaw
angle measurement cannot be calibrated using a similar technique. A method for the
calibration of the yaw angle sensor and for the calibration of the airspeed at non zero yaw
angles is therefore proposed.
The ambient wind measurements are made using anemometers mounted on the boom
extending a distance of 1.5 metres in front of the vehicle, and are therefore affected by the
pressure field in front of the vehicle. The extent of this pressure field is determined by simple
vehicle shape parameters. The calibration is required to correct the observed reading to the
freestream condition. Two methods for obtaining a general calibration are proposed. A series
of tests conducted in the wind tunnel, using a range of different vehicle shapes, tested at a
number of different speeds and yaw angles, may be used to develop calibration factors based
on the vehicle frontal area; this calibration can then be applied to any vehicle. Alternatively,
similar data could be generated using a computational fluid dynamics package. The second
method is preferred because a wider range of shapes can be analysed, it is less costly, and
there are no problems which may be associated with the wind tunnel walls.
8.5 DriveIine losses in coast down
A sample of the driveline losses were shown in table 8.2 to demonstrate the improvement in
the measurements achieved when the more accurate wheel torque meters were used. To
complete the information from the main study the driveline losses measured during all the
coastdowns in the main study have been analysed to determine coefficients which can be
compared with the main, mechanical and aerodynamic drag terms.
121
Results and discussion - An advanced coastdown method.
The use of a linear function with speed is the standard model when driveline losses are
measured in laboratory tests, and subsequently used in coastdown analysis. But for the test
vehicle used in this work they were modelled significantly better using a quadratic function,
with the improvement in RMS error for a single coastdown being of the order of a factor of
five. The results for the complete set of coastdown tests are given in table 8.12. The term in
speed squared is a significant one so the use of the simple linear function would, in this case,
lead to error in all three coefficient (AD BD and CDo) if it was used in the analysis of
coastdown data. The coefficient At is approximately 20% of the constant tyre drag term (AD)'
Bt is of similar magnitude to the speed dependent tyre term (BD) and C; is approximately 5%
OfeDo·
Summary of driveline loss results.
Two term analysis
Weighted Standard
average error
Standard
deviation
At(N) 25.5 0.020 (0.08%) 2.50 (9.8%)
Bt(Nsm-1) 1.41 0.12 E-2 (0.08%) 0.048 (3.4%)
Three term analysis
Weighted Standard Standard
average error deviation
At (N) 21.0 0.034 (0.16%) 2.28 (10.8%)
B t (Nsm-1) 2.09 0.45 E-4 (0.0%) 0.116 (5.6%)
C t (Ns2m-2) -0.02 0.13 E-3 (0.65%) 0.0034 (17.0%)
Table 8.12
Further work on the analysis of the transmission losses must be undenaken to develop a
suitable model for generating the driveline losses in a simulation program; the model must
122
--~--~~~-~---~~--------
Resulls and discussion - An advanced coasltiown melhod.
take into account speed, drive line temperature, and transmission load.
8.6 Summary of results
A summary of all the drag coefficients for the test vehicle are summarised in table 8.13 with
the 95% confidence limits calculated using equation 8.1 and the percentage contribution to the
total drag at 50 mph. The results are also plotted in figure 64 to show the relative magnitudes
of the contributions throughout the speed range. The value of CDO of 0.390 compares with a
value of 0.401 in the wind tunnel, a difference of 0.011 (2.7%). Carr [1] showed a difference
of between 0.007 and -0.011 for five European wind tunnels on a similar vehicle to the one
tested in this work.
Summary of results for the test vehicle
Tyres An = 0.0094 ± 1.6% 35.4%
BD (sm-I) = 0.217E-3 ± 7.6%
Aerodynamic CDo = 0.390± 1.5% 49.4%
KD = 0.977 ± (36%)
Transmission At(N) = 21.0±5.4% 13.3%
Bt (Nm-I s) = 2.09±2.8%
~(Nm-2s2) = -0.02± 8.5%
Undriven Au(N) = 3.24±5.0% 1.9%
wheels Bu(Nm-Is) = 0.235 ± 5.4%
Table 8.13
123
Conclusions and recommendations
Chapter 9 Conclusions and recommendations Page
9.1 Conclusions 125
9.1.1 Mathematical model 125
9.1.2 Application of on-board anemometers 126
9.1.3 Simulation program 127
9.1.4 Comparison of coastdown and steady state methods 127
9.1.5 Advanced drag measurement method 128
9.2 Recommendations for further work 129
124
Conclusions and recommendations
9.1 Conclusions
Using sophisticated instrumentation on board a research vehicle to measure vehicle speed,
driven wheel torque, engine torque and ambient wind conditions it has been possible to
quantify the principal parameters in a mathematical model describing the forces acting on the
vehicle when travelling in a straight line. Computer aided analysis of the measured data
enables the operator to separate the total drag into its various components and to establish the
confidence levels in the results obtained.
In developing the techniques employed it has been necessary to investigate the following
aspects of the research programme in detail.
9.1.1 Mathematical model
A comprehensive mathematical model for a vehicle travelling in a straight line in the presence
of ambient wind has been developed. The model includes tyre losses as a function of load
and speed (with a correction for ambient temperature), the transmission and un-driven wheel
losses, and aerodynamic forces.
The tyre loss model used consists of a constant plus a linear function of speed, but this may
not be appropriate for speeds above the maximum used in these tests (70 mph) because of a
large increase in tyre losses at high speeds. The influence of tyre inflation pressure was
minimised by always testing with the same cold inflation pressure so this was not included in
the model. The effect of the applied torque was assumed to be negligible at the loads
experienced in these tests.
The transmission losses are not included in the equation when the steady state test is being
considered because the drag is measured at the wheels. In coastdown they were measured
directly using the wheel torque meters and included in the analysis in the form of a look-up
table. The direct measurement of the transmission losses using wheel torque meters, and the
use of a look-up table is the preferred method for including the transmission losses in the
coastdown analysis, because it avoids the introduction of errors which can occur when a
simple empirical model of the coastdown transmission losses is used. However the penalty
of the method is the change in the aerodynamic drag caused by the wheel torque meters. If
this change in the aerodynamic drag is to be avoided then a model of the transmission losses
as a function of speed and transmission oil temperature must be developed, and the drive line
125
Conclusions and recommendations
loss coefficients detennined in separate tests.
The aerodynamic effects include the aerodynamic drag as a function of relative airspeed and
yaw angle, which allows for realistic ambient wind, and the effect of aerodynamic lift on the
tyre losses. It was shown to be unnecessary to include in the model changes of angle of
attack or the effect of aerodynamic side-force on the tyre losses.
The mathematical model has been formulated to allow the use of an original analysis to
detennine the variation of the aerodynamic drag coefficient with yaw angle in addition to the
standard drag coefficients.
9.1. 2 Application of on-board anemometers
Standard test methods, which do not measure the local wind vector, have been shown to
have inherent errors and to be unsuitable for separating the different sources of drag. It is
therefore necessary to measure the localised wind vector at the vehicle, which has been
allowed for in the development of the mathematical model.
Prior to testing the anemometers are mounted on a boom extending 1.5m in front of the
vehicle. In the case of the test vehicle used here this took approximately 30 minutes. As the
anemometers are positioned within the pressure field generated in front of the vehicle they
must be calibrated on the vehicle in order to detennine the true freestream conditions. It has
been established that the vane over-reads the yaw angle and the cup anemometer under-reads
airspeed. The calibration used is a combination of measurements in the MIRA wind tunnel
and tests conducted at the test track.
The increase in CDo caused by the external instrumentation (wheel torque meters plus the
anemometers) is 4.1 %. A large proportion of this may be attributed to the wheel torque
meters and could be eliminated by the adoption of non-intrusive transducers.
The results obtained when the anemometers were employed were shown to be more accurate
and repeatable than the standard methods, both for determining the total drag and for
separating it into its components. From tests conducted in relatively high ambient wind the
test to test spread of results is reduced by a factor of 4 for the constant tyre coefficient (AD) .
and the zero yaw angle aerodynamic drag coefficient ( CDo) and by a factor of 7 for the speed
dependent tyre loss term (BD) with the application of on board anemometers.
126
Conclusions and recommendations
9.1. 3 Simulation program
Using a digital simulation program of the vehicle coasting on a flat track in the presence of
wind, realistic coastdown data with known coefficients, ambient wind and noise has been
generated and used to validate the analytical software. It has been shown that the software
operated satisfactorily in the presence of measurement and system noise, and that the
dynamic characteristics of the anemometers have a small effect on the results.
The sensitivity of the velocity profile to each of the four parameters in the optimisation was
found using the simulation program. This is a measure of the ease with which each
coefficient can be determined from the raw data. In order of decreasing sensitivity they are:
Coo, Ao, Bo and Ko. The sensitivity of Ko was shown to be dependent on the range of yaw
angles encountered during the test This indicates the need to test in windy conditions if Ko is
to be accurately determined, contrary to normal practice where testing must be performed in
as little wind as possible.
The levels of repeatability predicted by the simulation study were not achieved in the actual
tests, the reason for the difference was attributed to sources of noise not included in the
model, for example, track surface irregularities, tyre temperature variation during the test,
noise in the driveline loss data, and to imperfect modelling of the forces acting on the vehicle.
A practical example of the latter is the influence of relatively small scale wind variations on
the aerodynamic drag.
9.1. 4 Comparison of coastdown and steady state methods
The coefficients determined from coastdown and steady state data can be directly compared
because the analytical method used takes account of the transmission losses. The values of
the coefficients obtained in the two test modes are comparable, with a slightly higher overall
drag in steady state mode. This JIlllY be due to the increase in tyre losses associated with the
higher torque being transmitted, a factor which was not included in the mathematical model.
Steady state testing proved to be the more difficult procedure to perform in practice. Results
obtained were significantly less repeatable from test to test After the conclusion of the initial
study the emphasis of the work was shifted to the further development of the coastdown
127
Conclusions and recommendations
method.
In addition to the main analysis the transmission losses were also analysed to obtain the
-transmission loss coefficients. Transmission losses were measured in coastdown using the
wheel torque meters, and in the steady state mode by measuring the transmission input and
output torques. In coastdown the driveline losses are repeatable from test to test, and are
.represented well by a quadratic function of speed. In steady state mode the losses were not
consistent and therefore require further investigation, however the average results show that
the loss is higher than in coastdown, but is not dependent on speed.
Driveline oil temperature (though not used in the analysis) was measured during the
coastdown testing so it may be possible to develop a more comprehensive model for these
losses in.the future .
. 9 .. 1. 5 Advanced drag measurement method
The advanced drag measurement method, based on the coastdown test, is designed to be a
flexible tool for the assessment of vehicle drag. Using the facilities in the software the
operator can select the level of complexity required in the analysis and hence tailor the test
and analytical procedure to the particular application. The use of the method to extract a single
parameter (total drag at 50 mph), the tyre losses, or the three main drag coefficients (AD, BD,
and Coo) has been demonstrated; and a novel method which also determines the variation of
aerodynamic drag with yaw angle (Ko) has been implemented, with the long term aim of
eliminating the requirement for wind tunnel tests completely.
At its simplest level the advanced method can be used to determine the total drag at a given
speed. From the results of all the coastdowns in the main study the total drag on the test
vehicle is estimated to be 436N ±O.87N at the 95% confidence level. The total drag at 50
mph can be determined to within 1% with a confidence of 95% from a single pair of tests.
The advantages of using a constrained analysis (ie. when one of more of the coefficients are
fixed in the analysis) when only comparative information is required have been
demonstrated. The example used shows that the total tyre losses can be determined to within
1 % at the 95% confidence level from 6 pairs of coastdowns. The number of tests required to
identify changes in the tyre loss coefficients (AD and BD) are also substantially reduced over
the unconstrained method.
128
Conclusions and recommendations
In the three tenn analysis (which has only Ko fixed) the tyre loss constant (Ao) and the zero
yaw angle Coo can be detennined to within 1 % and Bo to within 5% at the 95% confidence
level from approximately SO tests.
The most advanced method used is original because in addition to the three coefficients Ao.
Bo and Coo the variation of aerodynamic drag with yaw angle (Ko) is also determined. It is
therefore unnecessary to determine this parameter in a wind tunnel prior to testing. The main
test results which were conducted in low wind conditions showed considerable spread in the
value of Ko. as had been predicted by the simulation. Results for the three coefficients Ao Bo
and Coo were not significantly changed by the inclusion of Ko as a variable in the analysis
showing that when the wind levels are low the low sensitivity of Ko renders it unimportant.
Using data acquired in higher levels of wind the standard deviation in Ko was considerably
reduced. The mean estimate of Ko detennined was 60% higher than the value determined
from the wind tunnel. but it was shown that this represented only a small error in tenns of
yaw angle and is in part due to the crude method of calibration used.
The results from all the tests conducted on the Ford Escort are summarised in table 9.1.
Summary of results for the Escort 1300L
Coast down Steady state Wind tunnel
AD 0.0094 ± 1.6% 0.0110 ±7.6%
BD (srn-I) 0.217E-3 ± 7.6% 0.20SE-3 ±131.7% CDo 0.390± 1.5% 0.410 ±12.9% 0.401
KD 0.977 ± (36%) 0.614
At(N) .21.0 ± 5.4% 36.3±44%
Bt(Nm·1 s) 2.09±2.S% 0.0 ±(0.93N)
Ct (Nm-2s2) -O.02±S.5%
-Au (N) 3.24±5.0% 3.24±5.0%
Bu (Nm-Is) 0.235 ±5.4% 0.235 ± 5.4%
Table 9.1
129
Conclusions and recommendations
9.2 Recommendations for further work
1. The results obtained in this work are for a single vehicle, further tests on a range of
different cars are required to prove the general application of the method.
2. Anemometer calibration methods are considered to be somewhat crude using the current
methods. It is therefore reco=ended that additional work is conducted to investigate
the calibration methods. Two methods for developing a more suitable calibration
technique have been proposed. The preferred one is to obtain calibration data using a
computational fluid dynamics package for a range of basic vehicle shapes and frontal
areas, and hence develop a suitable correction method.
3. The anemometers used did not exhibit a symmetrical calibration curve about zero yaw
angle. This is attributed to the mounting of the anemometers and could therefore be
eliminated by using an instrument which combines the airspeed and yaw angle sensors
into a single unit.
4. To reduce the effects of external instrumentation on the measured aerodynamic drag, it is
suggested that non-intrusive torque meters be used.
5. A considerable amount of driveline loss data have been acquired during coastdown tests
and a rudimentary analysis performed. Using these data and the known transmission
temperatures a more comprehensive model may be derived.
6. Tests to establish the steady state driveline losses are required to generate a complete
model of all the losses on the vehicle for use in performance simulation studies. These
could be performed on the Department of Transport Technology chassis dynamometer.
Tests using the dynamometer can be performed over a range of speeds and loads.
7. Further testing in windy conditions with the improved torque meters is required to
confirm the suitability or otherwise of the coastdown method for determining the on
road CD<",) characteristic.
. 8. Several methods of modelling the tyre losses were proposed, and a linear function with
speed used in the analysis. Alternative models, for example with higher order speed
terms may be more suitable if testing is to be conducted in excess of the 70 mph used
here.
130
I Conclusions and recommendalions
9. The aerodynamic drag coefficient was assumed to be constant over the range of
Reynolds numbers encountered during testing. The validity of this assumption has not
been tested but could be assessed by calculating the drag coefficient in a number of
different speed bands.
10. The aerodynamic admittance frequency of the vehicle has been mentioned but further
consideration of the effects of relatively high frequency wind variations has not been
considered in detail, this may be a source of noise in the measured data and therefore
requires further attention. Additional test data is required to allow a detailed frequency
analysis of the ambient wind, and the vehicle response.
11. As the levels of accuracy predicted by the simulation were not achieved in practice a
more comprehensive simulation is required to investigate the possible sources of error.
12. The optimisation method used in the analysis of coastdown data considers each
coastdown run in isolation, in the four term analysis there may be some advantage in
analysing the coastdowns in groups as this will fill more of the optimisation space. It is
suggested that this approach is considered.
13. The growth in availability oflow cost data acquisition hardware and PC's for use in a
vehicle now make it possible to build an integrated data acquisition and analysis package
for use at a test track. In future work it is proposed to develop a system of this type,
which employs the methods described in this work, and some of the additional
proposals indicated in these recommendations.
~---------131
'~--'----- -- --- --
References and Bibliography
References
1 Carr G.W. Correlation of Aerodynamic force measurements in MIRA and other
automotive wind tunnels. Society of Automotive Engineers technical paper, SAE
821374 (1982)
2 EEC directive 88/436. Provisions relating to measures to be taken against air pollution
by gases from positive ignition engines of motor vehicles. (1988).
3 Roussillion G, Marzin I.L., Bourhis I., Lefeuvre I.C., Contribution to the
. improvement of on-road measurement of Cx by the coastdown method. MIRA
translation 62[79. (published in: Ingenieurs de 'Automobile, September 1978.)
4 Lucas G.G. Vehicle performance calculations. PhD thesis, Loughborough University
of Technology, 1970.
5 Emtage A.L. The vehicle coastdown test. MPhil thesis, Loughborough University of
Technology 1983.
6 White R.A., Korst H.H. The determination of vehicle drag contributions from
coastdown tests. Society of Automotive Engineers technical paper, SAE 72099 (1972)
7 Dayman B. (Ir), Effects of realistic tire rolling resistance upon the determination of
aerodynamic drag from road vehicle coastdown tests. 2nd AIAA symposium on the
aerodynamics of sport and competition vehicles. (1974).
8 Roussillion G, Marzin I.L., Bourhis I. Contribution to the accurate measurement of
aerodynamic drag by the deceleration method. Br., Hydrodyn. Res. Assoc. Advanced
road vehicle aerodynamics. paper 4, 1975.
9 Buckley F.T., Marks C.R., Walston W.H. Analysis of coastdown data to assess
aerodynamic drag reduction on full scale tractor-trailer trucks in a windy
environment Society of Automotive Engineers technical paper, SAE 760850 (1976).
10 Eaker G.W. Wind tunnel-ta-road aerodynamic drag correlation. Society of Automotive
Engineers technical paper, SAE 880250 (1988).
---------- 132 --------
--------
References and Bibliography
11 Ivens 1., Lawser 1.1. Experimental test track methods of estimating vehicle tractive
resistance. FISIT A paper 845105 Vienna 1984.
12 Schiirman D., 10hnsson L., Berg W., Calibration of chassis dynamometers for
emission and fuel economy testing using wheel torque meters. Society of Automotive
Engineers technical paper, SAE 800400, 1980
13 ECE Regulation number 15.05. Uniform provisions concerning the approval of
vehicles equipped with a positive ignition engine with regard to the emission of
gaseous pollutants by the engine. Economic commision for Europe, Inland transpon
commitee, Trans/scl/wp29/r.204 (1988)
14 Waiter I.D. and F.S.Conant, Energy losses in tyres. Tire Science and technology
November 1974, pp 235-260.
15 Barson C.W. Private communication with Dunlop U.K.
16 Schiiring D.l., Siegfried 1.F., Hall G.L. Transient speed and temperature effects on
the rolling loss of passenger car tires. Society of Automotive Engineers technical
paper, SAE 850463, 1985.
I 17· Fogg. A. Measurement of aerodynamic drag and rolling resistance of vehicles.
\ Congress Fed. Int. Soc.lng. FISITA proceedings 1964, pp 123-139.
18 Passmore M.A., lenkins E.G. A comparison of the coastdown and steady state torque
methods of estimating vehicle drag forces. Society of Automotive Engineers technical
paper, SAE 880475, 1988.
19 Morelli A., Nuccio P. Visconti A., Automobile aerodynamic drag on the road
compared with wind tunnel tests. Society of Automotive Engineers technical paper,
SAE 810186. 1981.
20 Clark SK. (ed), Mechanics of pneumatic tires. US department of transponation.
National Highway Traffic Safety Administration. DOT HS 905 952. Aug 1981.
21 Cuniss W.W. Low power loss tyres. Society of Automotive Engineers technical
paper, SAE 690108, 1969.
133
References and Bibliography
22 Smith J.R., Tracy J.C., Potter D.S., Tire rolling resistance - A speed dependent
contribution. Society of Automotive Engineers technical paper, SAE 780255,1978.
23 Yasin T.P. The analytical basis of automobile coastdown testing. Society of
Automotive Engineers technical paper, SAE 780338.1978.
24 Ivens J. The rolling resistance of some 13 inch tyres and the correlation between rig
and road. Society of Automotive Engineers technical paper, SAE 870422, 1978.
25 Passmore M.A. Coastdown test assessment. Confidential report to Ford Motor
Company. TT89 R 01. 1989.
26 Dorey R, McCandhish. The modelling of losses in mechanical gear trains for the
computer simulation of heavy vehicle transmission systems. Institute of mechanical
engineers, paper C190/86, 1986.
27 Hucho W.H. (ed), Aerodynamics of road vehicles. Publishers: Butterworths 1988.
28 Cooper R.K. Atmospheric turbulence with respect to moving ground vehicles. Joumal
of wind engineering and Industrial aerodynamics Vol 17 pg 215-238, 1984.
29 IDM electronics, Basic slip ring design. Technical data sheet 1984.
30 Fritschen L.J and Gay L.W. Environmental instrumentation. Publisher
Springer-Verlag 1979.
31 Hales F.D. Vehicle dynamics undergraduate couse notes. Loughborough University
of Technology. Department of Transport Technology. 1984.
32 Numerical Algorithm Group. Mathematical subroutine library documentation 1988.
33 Maclean.D. , Gust load alleviation control systems. A feasibility study. Department of
Transport Technology report 7606. 1976.
134
References and Bibliography
Bibliography
a Press w'.H., Flannery B.P., Teukolsky S.A., Vetterling W.T., Numerical Recipes -
The an of scientific computing. Cambridge University press. 1986.
b Bevington P.R., Data reduction and error analysis for the physical sciences.
MCOraw-Hill book company. 1969.
c White R.A. and H.H.Korst, A generalised method for determining drag coefficient or
rolling resistances from coastdown tests. 2nd International symposium on road vehicle
aerodynamics. 1974.
d Chapin C.E. Road load measurement and dynamometer simulation using coastdown
techniques. Society of Automotive Engineers technical paper, SAE 810828, 1981.
e Morimitsu N., Nakagawa S., Development of a simplified coastdown method for road
load calibration. Society of Automotive Engineers technical paper, SAE 840471,
1984.
f Korst H.H., White R.A., Aerodynamic and rolling resistance of vehicles as obtained
from coastdown experiments. Proc. 2nd International conference on vehicle
mechanics. Paris 1971.
g Dayman B. Jr., Tyre rolling resistance measurements from coastdown tests. Society
of Automotive Engineers technical paper, SAE 760153, 1976.
h Evans E.M., Measurement of the aerodynamic and rolling resistances of road tanker
vehicles from coastdown tests. Proceedings Institution of Mechanical Engineers. Vol.
198D No. 11. 1984.
i Korst H.H., Funfsinn M.A. Determination of effective rolling resistance by
coastdown experiments on smooth and rough roads. SAE publication P74.
pp133-141.
J Clark S.K., Schuring D.J., Interlaboratory tests for tyre rolling resistance. Society of
Automotive Engineers technical paper, SAE 780636, 1978.
135 ~.-~- - --~ ----- ------- -- - ----- ---- ------~---
References and Bibliography
k Lippmann S.A., Oblizajek K.L.. Metters J.J., Sources of rolling resistance in radial
ply tyres. Society of Automotive Engineers technical paper, SAE 780258,1978.
I Smith N.P. Wind gusts measured on high speed roads. Proceedings of the Institution
of Mechanical Engineers. Vol. 187 3On3. 1973.
136
Appendix A
Appendix B
Appendix C
Appendix D
Appendices
Summary of sections ofECE 83/351 regulations pertaining to road load
measurement and setting of chassis dynamometer power absorption unit.
(Based on appendices 2, and 3 of the regulation)
On-board anemometry specification. (Manufacturers spec.)
Operating instructions for on-board data acquisition system.
Analytical integration of the coastdown curve.
137
Appendices
Appendix A Summary of sections ofECE 83/351 regulations pertaining to road load
measurement and setting of chassis dynamometer power absorption unit.
(Based on appendices 2, and 3 of the regulation)
A.I Introduction.
While carrying out this research programme the ECE 83/351 regulations were in force, a
revised version is currently being phased in, however the changes do not relate to the road
load measurement and chassis dynamometer simulation sections so this summary of the
present regulation is likely to stay in force for a further five years. The summary is taken
from appendices 2 and 3 of the regulations. Appendix 2 relates to the specification for and
calibration of the chassis dynamometer, and the objective of appendix 3 is To measure the
resistance to progress of a vehicle at stabilised speeds on the road and to simulate this
resistance on a chassis dynamometer '.
A.2 Test conditions.
The regulations lay down the conditions under which testing may be carried out, with
reference to: the test track, atmospheric conditions, vehicle preparation, test preparation,
instrumentation and test methods. Statistical criterion for the acceptance of the data are
prescribed.
A.2.I Test track
Test track inclination must be constant to within ±O.1 % and not exceed 1.5%. The track
surface must be dry.
A.2.2 Atmospheric conditions.
Reference conditions for ambient temperature and pressure are laid down without specific
tolerances but air density at the time of the test must not deviate by more than ±7.5% from
that at the reference conditions.
138
Standard pressure
Standard temperature
Appendices
Ps = 100.0 kPa.
Ts = 293.2 oK.
Wind velocity should be measured 0.7m above the ground and the following magnitudes
must not be exceeded:
Average wind speed
Peak wind speed
Crosswind component
A. 2.3 Vehicle preparation
vw
vwp
vx
=
=
=
3.0 ms·l.
5.0 ms·l.
2.0 ms· l .
The test vehicle should be in normal running order and adjustment and have been run in for a
minimum of 3000 km. The following must be set in accordance with the manufacturers
specification:
Wheels, wheel trims, tyres and tyre inflation pressure.
Front axle geometry.
Brake adjustment (elimination of parasitic drag).
Lubrication of from and rear axles.
Adjustment of the vehicle suspension and vehicle level.
A.2.4 Test preparation.
Vehicle reference loading should be set to the manufacturers specified unladen + I OOkg and
distributed so that the centre of gravity is midway between the front seats 'R' points.
Windows and any air conditioning vents must be closed and heating or air conditioning
systems in the off position. The test vehicle should be clean. Immediately prior to testing the
vehicle should be brought to normal running temperature.
A.3 Test methods.
Three alternative test methods are prescribed by the regulations including coastdown or free
deceleration tests and the steady state method
139
-- --- -- -------- -- -----" ----- -----------.- --- --- --- - - --- - ------
Appendices
A.3.1 Energy variation during coastdown.
Instrumentation must be used to measure time with an error of less than 0.1 seconds. and
speed with an error of less than 2%. Accelerate the vehicle to a speed 10 kph greater than the
chosen test speed (v), shift the gears to neutral. Measure the time t\ taken for the vehicle to
decelerate from v2=(v+~v) to v\=(v.~v) where ~v~ kph and repeat the test in the opposite
direction to obtain ~. Calculate the average time T \ from the runs in opposite directions.
Repeat the test a number of times to obtain values of Ti until the statistical accuracy of the
average is less than 2%. The average T is given by equation AI. Statistical accuracy is
defined in section A3.1
1 n
T = -~T. n . \ 1
1=
Al
Power absorbed at the speed v is detennined from the average acceleration and the vehicle
mass as in equation A2.
p = Mv~v SOOT
A.3.2 Deceleration measurement during coastdown.
A2
A similar technique is employed using this method to that in section A2.2.2 but the
deceleration is measured directly using a suitable device such as a gyro-stabilised platform,
using this technique the inclination of the track 9 is also detennined. The increment of speed
over which the deceleration is measured ~v is recommended to be O.Sms-l. Average
acceleration attributed to the speed v is calculated from A3. Repeat the test in the opposite
direction and detennine the mean r \.
I
y\ = ! J 1\ (t) dt - gsin9\ o
A3
A number of tests must be carried out until the average r (calculated as in equation AI) has a
140
1--- --------- --------
Appendices
statistical accuracy of less than 2% (see section A3.1). Average force absorbed is calculated
using equation A4.
F = Mr
Required instrumentation accuracy is :
Speed
Deceleration
Track Gradient
TlIIle
< 2.0%
< 1.0%
< 1.0%
< 0.1 seconds
A.3.3 Torque measurement at constant speed.
A4
Torque must be measured using an appropriate device located in the drive-line, accurate to
within 2%. Speed must be measured with an error of less than 2%.
Bring the vehicle to the chosen test speed v. Record the torque C(t) and the speed over a
period of at least 10 seconds. Determine the mean torque CT! using equation A5 and the
average CT for tests in opposite directions. Variations in measured torque and speed must not
exceed 5% in each second of the measuring period.
Ht-I
= ..!... f C(t) dt ~t I
AS
As a reflnement to the general torque test procedure the integrated torque over a variable
driving pattern may be determined by operating the vehicle with a deflned driving cycle.
A.4 Statistical test acceptance.
The tests described must be carried out until the stated statistical accuracy (p) of the average
for the relevant parameter is achieved.
141
-------- -_.- -- -- -~-- -
Appendices
p =
where X is the relevant average value.
The standard deviation s is detennined from equation A 7.
s = ! (Xi - X)
i=l n-l
A6
A7
The value of le is determined from table Al depending on the number of sample pairs used.
This statistical test ensures that the parameter used has a confidence interval of ±2% at the
95% confidence level.
A.S Dynamometer calibration.
In general the instrumentation used to determine the load on the test track must be used in the
calibration on the dynamometer, except in the case of the measurement using a
gyro-stabilised platform (A.3.2) where the dynamometers instrumentation should be used.
The setup procedure is the same for each calibration method, this involves installing the
vehicle on the dynamometer, adjusting cold tyre pressure as required for the rolls, adjust the
equivalent inertia of the dynamometer, and warm up the vehicle to normal operating
temperatures.
Ideally the dynamometer should be capable of simulating the vehicle loads from 10 to 50
kph. If this is not possible it is recommended to use a dynamometer with the characteristics
defined in appendix 2 of the regulation, this requires a cubic term with speed to simulate the
aerodynamic power. The brake load should be set to within ±5% of that measured on the
road at 50 kph using either the inlet manifold vacuum method, or one of those described in
the later sections.
A.S.I Energy variation during coastdown.
The tests performed on the road are repeated on the dynamometer (apart from the test in the
142
- --- .- -- - - --~ - -----------~--- - ----. ----~------ ---- _.---- -------
Appendices
opposite direction) as in section A.3.1, and the power calculated using equation A8.
p = I v flv
SOOT
Adjust the brake to meet the requirements noted in section A.S
A.S.2 Deceleration measurement during coast down.
A8
The power absorber setting is determined by measuring the force acting on the vehicle when
it is on the dynamometer and subtracting it from the force calculated from the road test. The
dynamometer power absorption unit must be set to meet the requirements of section A.S.
A.S.3 Torque measurement at constant speed.
Repeat the tests performed on the road, with the vehicle on the dynamometer (excluding the
test in the opposite direction), and adjust the brake to within the limits noted in section A.S.
143
------ - - --- ----- -
Appendices
Appendix B On-board anemometry specification. (Manufacturers spec.)
B.1.1 Micro Response Anemometer
The model 2030 Micro Response Anemometer is a highly responsive three cup anemometer
which utilises a photon coupled chopper to produce a pulse output with frequency
proportional to wind speed. The anemometer is used in conjunction with the 1220 signal
conditioning module, which provides an analogue signal output proportional to air speed.
Specification
Threshold
Accuracy
Distance constant
Range
Cup material
Turning radius
Body size
Weight
Mounting
Photon chopper current
Calibration:
B.2.1
low
high
Micro Response Vane
0.5 mph
± 0.15 mph up to 25 mph
1 % above 25 mph
1.52 m
0- 100 mph or 0 - 45 ms'!
0.004" stainless steel
97 mm
305 mm H x 70 mm diameter
1.1 kg
Direct to 15.9 mm o.d. shaft
20mA
0.0 mph
44.35 mph
0.0 V
2.217 V
The model 2020 Micro Response Vane is an analogue output wind vane. The vane is
equipped with a structural plastic tail with a durable aluminium filled plastic coating. A
precision potentiometer is coupled to th.e vane shaft to produce an analogue output
proportional to direction. An airfoil style counter-weight provides balance of the tail
assembly upon the shaft.
144
----------~-~---- ----~~-
Specification
Sensor type
Transducer
Threshold
Dead band
Resolution
Distance constant
Damping ratio
Potentiometer linearity
Bearing
Turning radius
Operating temperature range
Body size
Weight
Mounting
Calibration:
low
high
Appendices
Rotating vane
Potentiometer, (5000 ohm
make-before-break
single wiper, continuous turning)
0.5 mph
1.00 at 00
Less than 1.00
1.07 m
0.4
0.5%
Sealed stainless steel with synthetic lubricant
457 mm
-15 to 55°C
305 mm H x 70 mm diameter
1.13 kg
Direct to 15.9 mm o.d. shaft
00
3600
145
0.0 V
5.00 V
---- -- ---- - --._------ ------~ ~-------
Appendices
Appendix C Operating instructions for on-board data acquisition system.
C.1 Operating instructions.
C .1.1 Introduction
The on-vehicle data acquisition system is a menu-driven system designed for ease of use, and
a clear display of the parameters being acquired. This user guide is split into two sections, the
fIrst section is a step by step guide to using the system, from fIrst switching on to
transferring the acquired data down-line to the host computer. The second section is a
description of the general programming approach and the routines themselves.
C.1.2 Operation
Where a question from the computer is displayed on the screen the question is in italics in
these instructions.
(i) Switch on main power switch at rear of computer and front panel 'power on'
switch.
(ii) When the ODT prompt (@) appears type 50000 and the system software will
commence operation.
(iii) The start-up display appears, with the question Initialise System (YIN)?
Answer Y: The system will clear all data space and continue to step (iv).
Answer N: The system does not clear the data space and goes to step (iv).This step
must be used if previously collected data is to be retained.
(iv) A control menu appears on the screen and the user may select from the options
listed. Entering any of the codes transfers control to that program. The operation of
each of these programs is described below.
146
- -------------_. ----------- -- - --- -- -
Appendices
MENU
LOAD AND CONNECT ....•... 0
SEND DATA TO PDP ...•.••... l
ACQUIRE DATA .........•.•.... 2
ACCELEROMETER SETUP ... 3
SHUTDOWN SySTEM ......... 4
SELECT NEW DATA PAGE ... 5
Code 0 This program performs two functions, connection to the POP in order to use the
micro as a standard terminal, and transferring 'programs from the host PDP to the micro. In
some respects the two functions may be explained together because in order to transfer a
program contact with the host must be established. A physical link is made by connecting a
land line to the communication pon on the rear of the micro. Operation is then simple because
selecting option 0 makes the link, the user can then log in to the host.
Transferring a program from the host is performed by typing <CfRL Y> to obtain the
loading prompt:
Name of LSI system .....
The name of the program to be transferred is entered without its type suffix which is assumed
to be .SYS. A counter displayed on the screen shows that transfer is taking place.
Code 1 This program transfers data files created during testing from the micro to the POP
11. The user must be logged in to the system which can be carried out via option O. Selecting
option 1. generates the prompt:
Please switch off RTC • waiting -
DCL version.
147
Appendices
Check that the real time clock switch on the front panel is in the off position and press
<return>, the computer will display the filename and size and transfer it to the PDP. There is
also a counter here to show that the data is being transferred If there is more than one file the
prompt will appear between each file. When all the files are transferred control returns to the
menu display.The files that have been transferred are now stored on the main disc with the
file type suffix .ACQ. When multiple data pages have been used (see Code 5) the transfer
operates on the current data page only, to transfer the data from another data page that page
must first be selected (5).
Code 2 This is the main data acquisition program which allows the operator to sample data
from the installed instrumentation. The sampling rate is not user selectable and is set to 4 Hz.
Enter filename? Enter the filename under which the data will be stored.
Enter No. of channels? User must enter the number of channels to be sampled.
Enter starting channel number? User to enter the number of the first channel to be
sampled.
The channels are connected in the sequence described below:
0 = Engine torque
1 = Wheel torque meter (near side)
2 = Wheel torque meter (off side)
3 = Speed
4 = Airspeed
5 = Air direction
6 = Accelerometer
7 = .. 8 = .. 9 = ..
Example: If the wheel torque and speed are to be recorded then Number of channels = 3 and
starting channel number = 5. When the channel infonnation has been entered the display
changes to the data display setup:
148
~-~-~ --- ------- ------- ----
Appendices
Engine Torque (N.m) WheellOrque (N.m)
L R
Accelerometers (g)
I 2 3 4
Speed (mps) Annemomeuy Speed (mps) ¥.w Direction (0)
VerucIe coefficients A B C
•.... : .•. :-.-; ....•.. ; ....•....... ;; ... ;;.;.:.;.;.- Memory status Page
When 'G' is pressed the system will sample and display data from the relevant channels in
the relevant position on the screen. The prompt:
type G' to go is then replaced with: type'S' to stop.
When'S' is pressed data acquisition stops, the coefficients generated from the sampled data
are displayed on the screen in the bottom block of the page setup and the prompt becomes:
Data OK YIN?
The data acquired is saved or destroyed depending on the operators response, control returns
to the main menu after carrying out the request.
Note: The amount of data space remaining in the current data page is displayed on the screen
under memory status and the memory page number is displayed beside it. The counter
decreases as the acquisition program runs and the data space is used up. If the data space fills
up before the operator presses S to stop, then the program will stop automatically and display
the Data O.K. prompt. A different data page may then be selected by returning to the main
menu.
Code 3 This program allows the accelerometers connected to channels 6-9 to be set up
geometrically level its use is self explanatory. Sampled data is not recorded.
149
------- -- ------ ---
Appendices
Code 4 The computer may be switched off between runs to conserve the batteries but is
good practice to run code 4 to clear up any workspace. When restarting go through steps i )to
iii) and answer No at step 3 otherwise any previously recorded data will be lost. Then
proceed as normal.
Code 5 Memory management is used in the system to increase the space available for
storing data. when this option is selected the prompt is :
Menwry page No .......... ?
Six pages are available (0-5) the first five pages are 40 Kbytes, and page five is 32 Kbytes
the total storage is therefore 232 Kbytes. It is not necessary to completely fill a particular data
page before moving on to another one, but returning to a previously used page will overwrite
the data already contained there as soon as option 2 is selected.
(v) If several files of data are required then the acquire data option (ie. code 2 ) is run
each time control returns to the main menu and a different f!lename entered
C . 2 Details of the software.
C.2.l Software
The software is written as a set of sub programs which are linked through a menu program to
form a complete system. The arrangement of the memory of the computer is shown in
Figure Cl. The principal sections are :
(i) Vector region. This region contains the necessary information to act upon vectored
interrupts. Under program control these are set to interpret system errors and
programmed interrupts from other devices.
(ii) Stack. The stack is used as a temporary storage space for interrupt and subroutine
return addresses, the stack is also used transparently by the system functions
installed in the computer for use in the program.
(ill) Scratch block. Used for storage of system parameters, and string variables.
150
Appendices
(iv) Boot. Boot code is loaded low in memory where it can be addressed without
resource to the memory management functions.
(v) Data area. This area is for storing test data and is managed by Programs Header
andMmgt
(vi) Program section. This contains all the remaining software, ie. acquisition system,
file and memory management, and communication software.
(vii) Prom code. Used to load programs into the computer, including the actual system
described.!t is essential that this code is not corrupted so it is partially separated
from the main system. If the main programs are destroyed then they are reloaded
using this code.
(vi) I/O page. Reserved by the machine for I/O to the various peripheral devices.
This approach to the memory map was taken because the memory may be write protected
from the high address's down therefore the programs are stored at high address's. To
conserve space for the data the programs are written in MACRO 11 assembly language,the
entire program suite occupies less than 8Kbytes.
The main programs and subroutines are described below and their inter-relationship shown in
Figure C2.
C.2.2 Main programs
The main programs are linked through the menu control program when selecting a particular
option program control is passed to the relevant program via the necessary setup programs. A
number of general purpose subroutines are available for simple tasks. The description of the
software contained in the following sections is labelled by the code used to invoke it (ie
startup is 5000g acquisition is by code 2), routines called by the main function are included
as subsections.
151
Appendices
C.2.3 SOOOg
On startup a number of routines are initiated to control the system these are transparent to the
user.
C.2.3.! Boot
A boot program located at starting address 5000 is used to set up a skeleton mapped system
by initialising the memory management this allows program control to be transferred up into
the main program section which can only be addressed when memory management is
selected.
C.2.3.2 Program Error
Control is passed to the error monitoring program which initialises the error vectors and runs
the memory management routine. The initial startup page is displayed on the screen.
ACTION: Start up screen display
Initialise system including program Mmgt
Act on error interrupts
Initialising the system involves clearing the vector region, stack, and scratch block, apart
from the data control words NXTFll.. and NXIDAT, these are only reset if the user answers
'Y' to the Initialise system? prompt on the stanup page. The vectors are set as shown in the
table below with maximum priority level to ensure that they are acted on as soon as they
occur. In the event of an error causing a vectored interrupt the action taken is to display the
message in the bottom right hand corner of the screen.
152
--------- --- ------- ---- - - ----- -- --~--- ------- - -._------
Appendices
Address Message Error
004 INST c.P.U. error
010 RINST Reserved or illegal instruction
014 BPT Breakpoint trap
020 IOT Input/Output trap
024 Nomsg Power fail
244 FP Floating point error
250 MMU Memory management error
C.2.3.2.1 Mmgt
Subroutine Mmgt is multiple entry point depending on the calling routine. Its overall
function is to produces a full mapped system using the system variables PAGE and LIMIT,
and the memory management look-up table MMAP. Entry point from Error is at MMGT2
and uses the existing system values. Entry from the main menu when option 5 is required is
atNXTPAG.
C.2.3.3 Control
The Control program sets up the main menu and interprets the code entered by the operator
and passes control to the relevant location.
C.2.4 Code 0
Code 0 is used to load a program into the system or link to the host PDP 11/34. Control is
passed to subroutine Prom (author: E.D. Rodgers). In normal operation the program
simply takes every character received from the keyboard or from the host and passes it down
the relevant serial line (ie TTO and TTI). Before transmission each character is tested to
establish if it is a control Y if it is then it starts the program transfer procedure.
153
-- - -------
Appendices
C.2.S Code 1
Selection of option 1 is used to send acquired data down to the host Program control is
transferred to Send which is simply a driver for a system subroutine Snddat (author
E.D.Rogers). Snddat is a general purpose macro subroutine designed to be called from a
Fortran main segment; Send provides the necessary emulation to form the linkage. The
argument list required to transfer each file is set up in the scratch block by copying the data
from the header block and including the default arguments. The argument list is as below:
ARG:
DATA:
Number of arguments in the list
Address of first data point
Fll..ENAME: Address of name of file
NTafAL:
NCHN:
NSTART:
SMFFRQ:
FRQINC:
DATfYP:
Address of number of data values per channel
Address of number of channels
Address of starting channel number
Address of number of ADC scans per second
Address of sampling period
Address of number of bytes per data unit
Once the argument list has been set up the address of the argument list is put into the standard
fortran linkage register R5 (i.e. address of ARG) executing CALL Snddat then transfers the
data. When the data file is transferred Send checks to see if there is another data file to be
transferred and if necessary repeats the setup operation, otherwise a return to control is
performed.
C.2.6 Code 2
Option 2 selects the main data acquisition option but also invokes the file management routine
so that data is correctly stored.
C.2.6.1 Program Header
A header block for each" data file is required so that the data can be transferred to the host, the
header block includes the filename, number of data channels, and start address of the data,
154
- --- --- ._-- -- -- --- --- --- --- ----- ---- -- ~ --- - -
Appendices
the number of data points per channel is included after completion of the test. The first two
arguments are obtained by prompting the operator for input, and are then also used to setup
the acquisition itself. Program Header references the system variable NXTFll... and alters
NXTDAT.
C.2.6.2 Acq
Program Acq is the data acquisition program, important sampling functions are carried out
using clock driven, high priority interrupts to ensure that no data is lost. It consists of a
control section and a series of subroutines and interrupt service routines (lSR's). The priority
task is to service the analogue to digital convenor when an interrupt from the clock occurs.
The remaining tasks are screen update, storage space calculation and data processing. If there
is insufficient time to complete these secondary tasks the control section will allow blocks of
data to be skipped. Keyboard interrupts are enabled to remove the need to scan the keyboard,
the interrupts generated by the keyboard are then analysed by an ISR. The various
subroutines and interrupt service routines are outlined below.
C.2.6.2.1 Main Control Section
The main control sets up and controls the data acquisition display page, and controls the
secondary subroutines. During acquisition the main section determines what display
information must be discarded if the sampling rate is too high to display all the data and
places the cursor in the correct field for outputting the parameters calculated by Float.
C.2.6.2.2 Isr Adc
Invoked by a clock-generated interrupt, this routine samples the relevant channels using the
ADC, and stores them in consecutive memory space using the data pointer. The gain setting
of each channel is extracted from the control and status word look-up table (CSW).
C.2.6.2.3 Isr Exit
Invoked by a keyboard-generated interrupt. This routine analyses the character entered at the
155
Appendices
keyboard and takes the appropriate action. If the character is any other than'S' then no
action is taken and the program continues to run the priority is set below the ADC ISR so that
data is not lost whilst it is serviced. If the character is an'S' then acquisition of data is halted.
If the data is considered to be satisfactory by the operator the data is retained and the system
variable NXTFIL appropriately updated. A call to this routine may also be made directly by
the Memory monitor subroutine if the data space is full. in which event entry point EXIT2 is
used.
C.2.6.2.4 Subroutine Memory
This subroutine calculates the remaining data storage space and checks it against the system
variable LIMIT. if the data space is full then it calls the exit routine at entry point EXIT2.
otherwise the amount of space remaining is updated on the memory status field in the bottom
corner of the screen.
C.2.6.2.S Subroutine Float
This subroutine is used to conven the ADC 12 bit integer values into scaled floating point
values using the relevant factors in the floating point look-up table (SCALE). The scaled
value is stored in the scratch block for funher calculation and also convened to an Ascii string
for display. each value is sent to the field indicated by the main control section.
C.2.6.2.6 Subroutine Least
This subroutine carries out a standard least squares quadratic analysis of the data to obtain the
three coefficients AD. BD and CD' Temporary storage space is in the scratch block. The
coefficients are updated in the floating point scratch block for display by Disco.
C.2.6.2.7 Subroutine Disco
This subroutine is similar in operation to Float but is used to display the coefficients with a
greater number of digits' after the decimal point.
156
Appendices
C.2.7 Code 3
Set This program is used to help set up the accelerometers correctly. When the vehicle is
stationary on a level surface this program indicates the amount of pitch and roll on the
accelerometer plate. Its main sections are therefore an ISR for the ADC and a calculation and
display block. Further details are not given as the program is not relevant to this work.
C.2.S Code 4
Shutdown of the system is preceded by a clear up of all the temporary storage space and the
stack and the display of the close down page. All system variables are preserved~ A call to
Error is made to run the clear up section using entry point SUBINT.
C.2.9 Code 5
Code 5 transfers control to Mmgt described in section C.2.3.2.1 the entry point from the
main menu is at NXTPAG.
C.2.10 Service subroutines
In addition to the routines dedicated to particular subprograms there are two routines used
throughout the code for basic input output
C.2.10.1 Type
This subroutine sends Ascii strings to the monitor at the current cursor position. The ASCII
string must be pointed to by register RD, the subroutine terminates when a null byte is found.
C.2.10.2 Enter
This subroutine is used to read Ascii strings from the keyboard, store them at the target
157
Appendices
address and echo them on the screen. It also recognises the delete character and removes it
from the entered string.
158
Appendices
2 AO A2 I D.6 a = - --
Az 4~
~ Az D.7 =-M
e
y Al
D.8 =-2A2
substituting
z = v+y D.9
hence:
dz 1 UI0 = dv
equation D.4 may !hen be written as,
t = U11
This is a standard integral which has three possible solutions depending on !he value of a2.
The cases of a'?- :s; 0 are not generally required in practical coastdown, so a2 is simply tested.
For !he case of a 2 > 0 !he solution is :
t = U12
equation D.l2 may be rearranged to give v2 as a function of elapsed time:
160
----- -----
Appendices
Appendix D Analytical integration of the coastdown curve.
Assuming that the drag function may be represented by a quadratic equation of the fonn,
=
and assuming that the drag force is given by :
=
then:
dv
dv -M
e dt
= dt
Me
Integrating equation D.3 assuming initial time of zero,
= t
we may write,
= ~ [(v+y/ + al
where :
159
0.1
D.2
D.3
D.4
D.S
=
Appendices
v +y
[ (_I ) _ tan ( ex~t) ]
ex ex -y vI +y
1 + ( -) tan ( ex~t) ex
D.13
Equation D.13 is used to generate the theoretical coastdown curve.
161
-------- -------------~
0.6 2000
f ~
.§ 0.3 -E .. ~ Q
o o
Coastdown profiles. Data for Ford Escort 1300L (1983)
~ ~ ~
_.I V
V V
o 20
.., """'l .... ~ R
40
V V
~ ,...
60
Time
Figure 1
-'
~ .......
III Distance • Speed + Decelernrion
--..
80 100
40
20 ~
o 120
~
,-.. ., z· '-' -~ = "0 .-00 ~
~
20
10
0
·10
·20
Figure 2.
Residuals from fit to real data.
(Polynomial method of differentiation)
.30 L-~-L~~~~~~~ __ L-~-L~~~~~~
o 10 20 30 40
Speed (ms· l )
163
-~-------- --------- ----------- ----- --
------- --- -,'.
'" '" o .J
2
1
o 1
Figure 3.
General relationship between loss modulus
temperature and frequency of a typical tyre
compound.
10
Frequency (Hz)
164
.~-------- ._----
/' 20°C
40°C""
100
0.03
-c .S:!
<.J
if: Q) Q
U Q) <.J c
0.02 c:s -'" .r;; Q)
c:::: 0Jl .5 --Q
c::::
0.01
o
Figure 4.
Rolling resistance against speed. I I(after reference 21)
/ --'"
70 ISpeed (mph)
165
I I
/ I
I , i i
140
'" '" c -~
.S -'0 e:::
A'
Figure 5.
Rolling resistance of a radial car tyre as a function of
cavity temperature and speed.
B Coastdown
-- ---Cavity Teinperature
166
,-.. U 0 '-' ~ ... = -Cl! ... ~ c. E ~
Eo<
Figure 6.
Effect of temperature on rolling resistance
coefficient.
60
40
20
0
-20 0.005
........ ! "- "- I -Go Ambient
"l I ... Tyre Cavity
"'- ......... .........
i ....... !
........,
~ " N ..........,
r-J 1"--i--I --0... ! I , ,
I 0.009 0.011
Rolling Resistance Coefficient
167
-
0.015
-I: ~ .;:; E ~ 0
U ~ <.-I: <:a -OIl
·Vi ~
~ I:.Il .: --0 ~
0.07
0.05
0.03
0.01 -0.6
Figure 7. -
Effect of applied torque on rolling resistance
coefficient.
i I I
" i / ,
u I ! c: g ~ ,
I I "v;
I " ~ § ! 1
E i 11 "" ,
:s ! i I
~ / I
-0.4 -0.2 0.0 0.2 0.4 0.6
Braking Coefficient Driving Coefficient
168
Figure 8.
Basic airflow pattern around vehicle.
Freesrream flow Exaggerated
boundary Jayer Boundary layer velocity profiles
========~~~~~se~p=~ti~on~~~~~~~~ ------,-,
Turbulent wake
I
~-
point ~~~~;t~:::::== S CofP
169
~ CofG
(., .....
Figure 9.
MIRA wind tunnel force and moment convention
L
170
--- -- -- ---- ~- --- ---- - ---.-- ---- --- --- - -- - ---
----._-- -- - ----
Figure 10.
Velocity vector diagram.
v
171
.-.~ ._- ---- - ----- --.-. -----~ .. -- ---~ --- ---
1.5
1.0
Figure 11.
Variation of aerodynamic drag with yaw angle
for a typical car.
·30 o 30
Yaw AngleC)
172
~----~-- ~~ ---- --- - ---- - - ---'- ---- -- ------
Figure 12.
Calculated Ad against wind speed for various wind an.gles (unconstrained analysis)
.111311
e = 10 6
.0125 e = 30 + 8 = 50 >< 8 = 70 <>
.0120 8 = 90 0 - - - = 10% error
"Cl .0115
-<
.0110 - - - - - - - - - - h=-';=-';'7"':"~ - - -
.0105
.0100
o 1
-----
2 3
Wind Speed (m/s)
173
~---------- -----
4 5
- ------ - -
0 0 0 0 ,..., l<
't:l >Q
~~- - -------
4.5
Figure 13.
Calculated Bd against wind speed for various wind angles (unconstrained analysis)
9=10 £l.
4.0 9 = 30 +
3.5
3.0
2.5
2.0
1.5 o
-------
9 = 50 X
9 = 70 0 9 = 90 0
... = 10% error
- - - - - - - - - ----
- - - - - - - - - - -~~~--=--=---::-" -
1 2 3 4 5
Wind Speed (m/s)
174
-- - - ---- --- ------ - -------- -
"C U
[---------
Figure 14.
Calculated Cd against wind speed for various wind angles (unconstrained analysis)
0.42
0.40
0.38
e = 10 ~ 0.36 e = 30 4- - -- -- - - -
e = 50 X
e = 70 <> 0.34 e = 90 Cl
•• - = 10% error
0.32 0 1 2 3 4
Wind Speed (m/s)
17S
- ---~--- ------ ---- -------- ~-
5
30
o
--- - -- ---
8
Figure 15.
Yaw angle against vehicle speed
(ECE 15.04 regulations 'worst case')
16
... Hel!ldwi nd
+ Teilwind
24
Vehicle Speed (ms-I)
176
.1 V .. = 2ms
32
--------~-
•
40
4
3
2
1
o
Figure 16.
Variation of aerodynamic lift with yaw angle
for a typical car.
-45 o 45
Yaw AngleC)
177
------ ~~~ - - ---- ------ ---------- --- - --- --
Figure 17.
Vehicle tyre running at a slip angle.
~R
v
178
Figure 18.
Block diagram of vehicle instrumentation
179
3000
2000 c ~ r.. -00. =i.
1000
o
Figure 19.
Engine torque calibration.
.- , .- .- • Torque = Jl Strain / 23.63
Jl /' 1 1 I I I
I- Std. error = 0.055 ~
V -
/'
V /it' -
.la
I I /" ~
V f""
/'
1/ V
o 20 40 60 80 100 120
Torque (Nm)
1SO .
-~----~------ ~--- -- -~~-- ------------~--'---- --
Figure 20.
Wheel torque transducer schematic.
Stub axle arrangement bolts
on to wheel hub
Roller bearing
Wheel mounts to outer nange
181
Strain gauge mounting area
Outer top hat section
Figure 21.
Wheel torque meter system layout.
Aerials on wheel arch Power supply ror .!"!~!!!'!!!!!'!!!!!'!!!!!'!!!!!'!!'!!!I
rotati; electronics L...-____ ..,
Signal conditioning and transmitter
Transducers
Aerials on tyre
• Aerial seperation
appro)( 20cm
PIIEAMP
PREAMP
Preamps located under bonnet
Receivers (signal demodulation
votgae output)
182
Cl>
Cl z > t'"
<"l o Z
'" ::j :5 z Z '"' '" > <"l :0;
Signal conditioning (Power supply to receivers
filters output to computer ADC)
Figure 22.
Wheel torque meter calibration (1).
9
Vo = 0.0513 + 0.0233*Torque 6
x2=2.0mV ---;>
3 '-' -::: c. -::: 0 0 CIJ eJ)
"= -- -3 0 ;>
-6
-9 -400 -200 0 200 400
Torque (Nm)
183
- -- - -- --- ---- ----- - ---~- - --------------- -
Figure 23.
Wheel torque meter calibration (2).
Vo = -0.0270 + 0.0224*Torque
6 X2 = 2.0 mV ,.-, e: _ 3
= Co -= o 0 a.> OD ~ -Q
;> -3
-6
-9~~~~~~~~~~~~~~~~
-400 -200 0 200 400
Torque (Nm)
184
---- ----~- -- --------------
,-., .... • '" E '-'
Figure 24.
Vehicle speed calibration.
50 1 I I ! L7 _I-- Speed = 8.943 * Voltage
V 40
V 30 1 V 1
./ V
I .."Jlf '" I • 20
1/ i
A 10
/ , o o 1 2 3 4 5
Voltage (V)
185
------_._- -- --- -~---------- --- ---- _._------- ---- -- ---- --- -----
Figure 25.
Schematic of on-board anemometers
t'·-----·.· ---;;--____ _ I ('UA .. , .. , .<D'US)
i
I
,
m". ! -ao!JH: J--
,,-
• '-_.
186
1----- - -------
Figure 26.
Computer hierarchy.
MAIN FRAME HONEY WELL MUL TICS
Data analysis Presentation of results
Analysis of results
~ •
r r CHASSIS DYNAMOMETER HOST MINI
MICRO PDP 11 PDP 11/34
Chassis dynamo meter Data acquisition program development, data analysis, control and calibration presentation of results
• ~
r , . VEHICLE
LSI 11/23
Data acquisition Processing
187
Figure 27.
On-vehicle software.
CONNECT TO
HOST FILE --"
HANDLING MAIN -CONTROL PROGRAM
SEND DATA
I" TO HOST , USER
INPUT/OUTPUT
'I" , DISPLAY
r ROUTINES
ACQllSmON TEST & STORAGE . PROGRAMS . ROUTINES
FLOATING ~ POINT
SCALING ROUTINES·
DATA ANALYSIS ROUTINES
188
Figure 28.
Instrumentation data
Signal Conditioning Input Oucput Calibration Scale Mea.surand Transducer Telemetry Supply Voltage
Method Factor Accuracy (V) (V)
General Fillers range)
~trnin gauged Full Bridge 1Hz low pass 0-5 ±a.s Nm Engine I '\notion Slip Rings Strain gauge (Sailen & Keye ±15 (0-1 ()() Torque ann x20(Nm) Torque shaft amplifier 2nd order) Nm)
Frequency I 1Hz low pass 0-4 Steady Sloned disc Speed in :<8.943 ::0. 15mJs Vehicle + inductive Line Voltage (Sallen & Keye ±15 (0-36 lathe. Digital (m/s) Speed pickup Convenor 2nd order) m/,) tachometer
1Hz low pass 0-5 180 degs Excitation Set in line =2.5v =2 degs Rotating Line & Buffer (Sullen & Keye ±12 (±180 =180 degs ... 0.0139 Yawangle Vane amplifier 2nd order) degrees) degs
0-5 Manufact- ::O.07m/s Frequency I 1Hz low pass x8.943 «llmls) Relative Cup Line Voltage {SaHcn & Keye ±12 (0-45 urers (m/s) 1% Air-speed Anemometer Convenor 2nd order) m/s) cenificme (>llm1s)
94kHz F.~. Bridge
1Hz low pass x43.95 ::lNm Bolt on amplfier ±9 Balanced (Nm) Wheel train gauged Transmitter (Sallen & Keye
+12 (±400 Torque Torque Receiver 2nd order) Nm) ann X44.~} ::INm hub 119kHz F.~1.
Transmitter Demodulation (Nm
189
I ,
Figure 29.
MIRA wind tunnel installation.
WIND TUNNEL INSTALLATION
r FULL - SCALE WIND TUNNEl
~~~/ Chnis Dynlmam~tu
~ Control Rn ... /
Entry --.
Scale 1 : 700
190
hl,Ie, Strlighttntr
El'lctnia, BuUdllll
Figure 30.
Test vehicle in MIRA wind tunnel in base form.
191
Figure 31.
Test vehicle in MIRA wind tunnel with
instrumentation.
192
Vehicle Make Vehicle Model Vehicle Type Trim Height
Figure 32.
Aerodynamic characteristics for base vehicle.
(Configuration A)
Escort Overall Length 3970 mm l.lL Wheelbase 2395 mm 5 door saloon Track Front 1385 mm; Rear 1430 mm Front o nun; Rear Omm Frontal Area 1.33 sq.m
Horizontal Buoyancy Correction Applied to CD = -0.009
Yaw Force Moment Axle Load Angle Coefficients Coefficients Coefficients
Deg. CD Cs CL CMX CMY CMZ CYF CYR CLF CLR
0.0 0.385 -0.010 0.290 -0.001 0.025 -0.004 -0.009 -0.001 0.170 0.120
-25.0· 0.465 -1.119 0.667 -0.272 0.088 -0.166 -0.726 -0.393 0.421 0.246
-20.0 0.447 -0.866 0.647 -0.218 0.058 -0.167 -0.600 -0.266 0.382 0.265
-15.0 0.426 -0.631 0.539 -0.163 0.049 -0.149 -0.46-1 -0.167 0.319 0.220
-10.0 0.399 -0.423 0.407 -0.108 0.053 -0.108 -0.319 -0.103 0.257 0.150
-5.0 0.390 -0.201 0.329 -0.052 0.013 -0.062 . -0.166 -0.041 0.196 0.133
5.0 0.391 0.189 0.318 0.048 0.030 0.053 0.148 0.041 0.189 0.129
10.0 0.406 0.407 0.390 0.099 0.046 0.101 0.304 0.103 0.241 0.149
15.0 0.440 0.608 0.530 0.149 0.045 0.142 0.446 0.162 0.310 0.219
20.0 0.464 0.844 0.682 0.208 0.038 0.165 0.587 0.257 0.379 0.303
25.0 0.479 1.114 0.703 0.267 0.081 0.169 .. 0.726 0.388 0.432 0.271
193
Centre or Press.
XCP
14.9
19.3
23.5
25.5
30.2
28.3
24.7
23.4
19.6
15.2
Vehicle Make Vehicle Model Vehicle Type Trim Height
Figure 33.
Aerodynamic characteristics for instrumented vehicle.
(Configuration B)
Escort Overall Length 3970 mm l.3L \Vheelbase 2395 mm 5 door saloon . Track From 1461 mm; Rear 1430 mm Front o nun; Rear Omm frontal r\rea 1.85 sq.m
Horizontal Buoyancy Correction Applied to CD ":;; .0.009
Yaw Force Moment Axle Load Anl-:lc Cnefficients Coefficients Coefficients
Deg. CD Cs CL CMX CMY CMZ cn' CYR CLF CLll
0.0 0.401 ·0.013 0.273 -0.002' 0.031 -0.005 -0.012 -0.001 0.167 0.106
-25.0 0.491 -1.121 0.654 -0.268 0.088 -0.178 -0.739 ·0.383 0.415 0.239
-20.0 0.468 -0.873 0.629 -0.214 0.064 -0.177 -0.613 ·0.260 0.379 0.250
-15.0 0.455 ·0.627 0.515 -0.159 0.062 -0.153 -0.466 ·0.160 0.319 0.196
-10.0 0.422 ·0.415 OA07 ·0.103 0.053 -0.110 ·0.317 0.097 0.257 0.150
-5.0 0.412 -0.208 0.317 ·0.051 0.033 -0'()62 ·0.166 -0.042 0.192 0.126
5.0 0.409 0.186 0.297 0.045 0.028 0.051 0.144 0.042 0.176 0.120
10.0 0.426 0.387 0.383 0.091 0.043 0.100 0.294 0.093 0.234 0.148
15.0 0.456 0.595 0.530 0.143 0.043 0.146 0.444 0.152 0.308 0.222
20.0 0.481 0.841 0.667 0.203 0.040 0.174 0.595 0.247 0.373 0.294
25.0 0.486 1.101 0.662 0.259 0.080 0.181 0.731 0.369 0.411 0.251
194
Centre uf Press.
XC»>
15.9
20.3
24.4
26.5
29.8
27.4
25.8
24.5
20.7
16.4
---~
J 0.50 '-'
1:.11 e o .... c 0.45 -c ~ .y If ~ cS 0.40
Figure 34.
Coefficient of drag against yaw angle.
MIRA wind tunnel.
• St.endl9rd Vehicle
~ + Instru~entetion.
0.35 L-.l--..L..-.L-..L-"""",-----L---'----'--'----L---L---L.---'---'---'---'---'----''--L......J
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
Yaw Angle (rad)
195 -- --
Figure 35.
Coefficient of lift against yaw angle.
MIRA wind tunnel.
196 ---------------
- --------- ------- ---- -----
,-.,
'" U 0.8 '-'
Q,j c:.J ... 0 ~ Q,j
:9 cr.J. "-0 ... c Q,j
0.4
0.0
.0;:; -04 E· . Q,j o U -0.8
Figure 36.
Coefficient of side force against yaw angle.
MIRA wind tunnel.
• Stonderd Vehicle • + InstrulTlentl!ltion
-1.2 L.......L......L-..J..........L...-L----'---L--,----,-L--,--'L...-.,L,-.L......J..........L...-L----'---L--'---'
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
Yaw Angle (rad)
197
0.48 ---~ U -;; 0.46 ~
"'" Cl· '0 0.44 .-~ .-....
IS 0.42 ~
. U " 0.40
Figure 37.
Coefficient of drag against yaw angle squared.
Fit for ± 150
Fit for± 25°
,-/
/ / ,-
/.
/
MIRA wind tunnel.
/
,/ /
•
• Stand~rd Vehicle
• + IngtruPlentstion.
0.38 L-.L..--'---'---'----'---'---'---L.,---.1---L.----'-,.---l----'----'----'----'---'--'_L-.J
0.0 0.04 0.08 .0.12 0.16 0.20 .
Yaw Angle squared (rad2)
198
---------- -----~-- -- ----- ---- - ---- --- --- - --------
,.-. Q
u 0.50 '-'
... :; 0.45 = ~ .-(J
is ~ Q
,U 0.40
Figure 38.
Coefficient of drag.
Comparison of measured and model data.
• Measured in wind tunnel
X Model for CD .. cn. -t- 0.614 y~
• Model for Co .. Co. + 0.4581;12
0.35 '--:-o--'---'----'---'---':-----'---'-----,!-_ ---'----'_'---'---'----'---'--'-----'---'---'----1
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0,5
Yaw Angle (rad)
199
Figure 39.
Coefficient of lift against yaw angle squared.
MIRA wind tunnel.
0.7 Fit for ± 150 -.. ,-. Fit for± 250 -...
U .. '-' 0.6 0:= :.J ...
0.5 0 -J:::: Q,j .~
E 0.4 • Standard Vehicle Q,j
~ + Instru~entetion. 0 U
0.3
0.2 0.0 0.04 0.08 0.12 0.16 0.20
Yaw Angle squared (rad2)
200
1.2
1.0
'"':l S::2.. 0.8 ~ .-...::l '0 0.6 -C
11.1 .;j 0.4 IS
11.1 C
U 0.2
-- --~----
Figure 40.
Coefficient of lift.
Comparison of measured and model data.
.& Measured in wind tunnel
>( Model for CL = CL. + 3.64 W2
• Model for CL = Cr..,. + 1.78 W2 .
0.0 0.1 0.2· 0.3 0.4 0.5
Yaw Angle (rad)
201
Figure 41. --
Anemometer airspeed calibration.
Transport Technology open section wind tunnel.
o ~L-~~~~-L-L-+~~~~~L-~~~-L-L~~ o 5 10 15 20 25 30 35 40 45 50
Tunnel Airspeed (ms'!)
202
'7 25 OIl
5 '-'
~ 20 <U Co OIl r... .-..( 15 r... <U -<U
§ 10 5 <U
~ 5
Figure 42.
Anemometer airspeed calibration.
MIRA wind tunnel.
O~~~-L~~--L-~~-L~--~~~~~~--L-~~-"
o 5 10 15 20 25 30 35 40 45 50
Tunnel Airspeed (ms·I)
203
~ ~- -- ~-~---~~~~-- ----- - - --------:ij
Figure 43.
Anemometer calibration with yaw angle.
MIRA wind tunnel.
• 1.2 , , , , , , , , -C eu E f-eu ... ::: 1.1 f- + +. + + + + + en + + eo:: + eu ~ YI!IW angle + E f-
- f- + Air speed eu C C 1.0 f-::: --- f-eu -u
C-.-.c eu 0.9 - ~ ;> • • 0 -.: • • eo:: ~
0.8 , , , , , , , ,
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
Yaw Angle (rad)
204
Figure 44.
Anemometer yaw angle calibration.
MIRA wind tunnel.
• -0.5 L-~L--.'--L--.'--'--"--"---'---:--'-:--"--.J..,...-"--.L-.L--L--'-------:....I..-...L.....,-J -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
Tunnel Yaw Angle (rad)
205
1--------- --------- ---- -- ---- - -~ ----- ----
MeD.n headwind
Mean crosswind Turbulence mio
Scale length
Figure 45.
Simulation block diagram
Drydfn filler ,,,,'em
t Band limited while noise
Wind Vehicle dynlllnics
t Distance constant
206
Dis1:U1Ce consllnlS Damping ratio
Anemomeler dynamic:
characteristics
Equation or molion
Vehicle coefficients
"""''''' Vehicle coefficienu
Noise
Measured signals
Figure 46.
Spatial variation of the wind
v(l+tanf3)
v(l-tan[3)
South Position
North
W7
Figure 47.
Variation of RMS curve fitting error with Ko
0.20
(I. IS
0.16
(1. 14 ,.-. -in E 0.12
3 ms-I
'-" t-o 0.10 t-t-CIl
rn. (1.02
:;;; ~ u .lib 2 ms-I
It.CH
[1.02 1 ms-I
,0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 .-, - 0.2 0.9 1.0 1.1 1.('
Coefficient Ko
208
-- --- - - --- -------
Figure 48.
Simulated coastdown data.
30
,-., 20 -, '" E --- 10 ..., Q.l Q.l c-
oo ,-., 0
0 --Q.l -I:JJ = -10 eo: ~ eo: >- -20 x Vehicle speed
• Airspeed
• Yaw angle
-30 0 20 40 60 80
Time (s)
209
,-, -In E '-'
1:l. ~ Co
t:Il
,-, 0 '-' ~
'El c < ::: ~
>-
Figure 49.
Superimposed actual and measured airspeed and yaw
angle data from simulation.
30
20
10
0
-10
-20 Airspeed • Yawangle •
-30 0 20 40 60
Time (s)
210
80
-------. - ---- -- ---- ---------- --- ---------- --._-------- - --
30
----. 20 '" E '-' --~ ~ 10 c-
v:,
--- 0 0
'-' ~
"6ii = -10 <: ~ ~
>- -20
-30
Figure 50.
Data obtained during coastdown.
(Ambient wind within ECE 15.04 limits)
._---- -- - .. _--- ------
X Vehicle speed
• Airspeed
• Yaw angle
0 10 20 30 40 50 60
Time (s)
211
70 80
Figure 51.
Data obtained during coast down (high wind condition)
X Vehicle speed
·20 • Airspeed
• Vawangle
·30 o 10 20 30. 40 50 60 70· 80
Time (s)
212
-~, - - ~----~ ------- --- -------- .-----~---------
Figure 52.
Normalised residuals from curve fit to coastdown data.
;;' Q -~ '" ea = "C
'in ~ loo
"C ~
.~ ea E
(Low wind conditions)
I I I I I I I
1.33 -
0.67 I-
• # ° 0
~~ '0:: .... ~-: ... °0 : • I ~'.~. '. . .. _.::' .. ' o 00 . . ....... . .. ',~ \ ' .. - .. - .... : .:: .,. .... ~ .. , .'. • °0 ... .: ............ :.::'..... : • .:.~:- 0° •••••••• - ..... "0°. . . ........ 0: .
~ -0.67-;Z
--1,33 ~
I I I I I I I
r T
--
-
-
-
-
-
-I I
o 20 40 60 80 100
Time (secs)
213
Figure 53.
Normalised residuals from curve fit to coast down data.
(High wind conditions).
I I I I I I I I. I
1.33 I- -I- -
0.67 I-
-. • .' .0 ••
~~~~:/'~_~·:~,,~~:~·~:~~~~~~~~~~~~~i~;:~~~~~_~.~.~~~\~~~~\'~:'~'------4 0.00 • I. ' ... ;: :i.', '. . • .,;. •. , :;, ,'':.' / .' . • .. .:' . :: ...... ~.. . ..' .
• • ,0 •
-~
E ~ -0.67-Z
-
- --1.33 - -
I I I I I I I I I
o 20 40 60 80 100
Time (secs)
214
Figure 54.
Uncorrected steady state data
750
t ± I Standard deviation
Z 600 '-'
150
o 5 10 15 20 25 30 35 40
Speed (ms· l )
215
- -~-------- --- ------ -- -------
Figure SS.
Corrected steady state data.
900.F ~-.--.-r-.-.--.-.=. ,··==r=-r··~·T··=-'·--,-,-,
750
,.-.. 600 2: '-'
~ r.. 450 ~ eJl
E ~ 300
150
o
! .. ±. I Standard deviation
5 10 15 20 25 30 35 40
Vehicle Speed (ms-I)
216
-- -~- -- ----------- ~----- ------- --- -----------
Figure 56.
Normalised residuals from curve fit to steady state data.
0.10 I , I I T I I I I
0.08 r- -
0.06 !- -0.04 - -
'" -; 0.02 = "0
... -·iii ~ I. 0.00 "0 ~
'" .- -0.02 -= r- I -5 I. Q
-0.04 Z !- --0.06 I- --0.08 t- Error bars representing ±1 std. dev. --0.10 I I I I I I I I I
o 8 16 24 32 40
Speed (ms·1)
217
------ -- ~--~------- - -~ ---------~-------- --- - - - -- - - - -- - -
750
600 Z '-' ~
~ 450 .E ell
f Q 300
150
o
Figure 57.
Steady state test data.
(Runs in opposite directions averaged)
t ± I Standard deviation
5 10 15 20 25 30 35 40
Vehicle Speed (ms·I )
218
-------- --- ------- - - --- ---- ---
120
100
,-.. 80 Z
'-' Q.>
"" r.. .;: 60 e.!I e\l r.. Q 40
20
o
- -------~-~
Figure 58.
'Offioad' driveline drag measured during a single
coastdown test.
5 10 15 20 25 30 35
Vehicle Speed (ms·I )
219
~ -----
40
Figure 59.
Corrected steady state test data, showing the
driveline losses.
900
• Engine torque X Wheel torque
675 . • Driveline loss
225
o 10
. ----_._---- -- --- ~ --- - ---- --~ - -- -
•
20 . 30 Vehicle Speed (ms·!)
220
---._---- -- --- -, - - ------- -
40
Figure 60 .
. 'Onload' driveline drag measured during steady state.
120
100 ~ ± I Standard deviation
,.-, 80 Z '-' ~ u ...
60 ' 0 .... OJI
E ~ 40
f 20
o 5 10 15 20 25 30 35 40
Vehicle Speed (ms· l )
221
~
Z '-'
a.> ... r..
.E e.o ~ r..
Q
12
10
8
6
4
2
Figure 61.
Undriven wheel losses against speed for a single
wheel.
o L-~~J-~-L~~~L-~J-~-L~~ __ ~
o 5 10 15 20 25 30 35 40
Vehicle Speed (ms·I )
222
Q U -C a.> .c:; E
a.> 0 U
Figure 62.
Co(\jf) characteristic determined from coastdown data
and the wind tunnel.
0.55
Wind tunnel x
0.50 High wind levels ... Low wind levels •
0.45
0.40
Yawangle Cl
223
Q
U ell --Q.l
Cl
Figure 63.
Comparison of the yaw dependent component of
aerodynamic drag derived from coastdown and wind
tunnel data.
0.100
Wind tunnel x
0.075 High wind levels "-Low wind levels •
0.050
0.025
Yaw angle n
224
---------------- -- ----- --------- ------
Figure 64.
Contributions to vehicle drag.
:008
'?88
300
,-.. :,0 Z '-'"
Q,j &80 I i Y ... I-.g SOO 0Jl ell I- 400 0
i
300
If! !5 '1C '.'
Speed (mph)
225
Figure Cl.
On-board computer memory arrangement
77777 7
76000
75700
14000
64000
52000
40000
26000
14000
0200 0
0050 3
00500
0010
0004
0000
0
0
0
VD PAGE
PROM CODE
SYSTEM PROGRA.\t:S
PAGE 5 J2kB
PAGE '" ,"OR
PAGE 3 .aOkB
PAGE 2 JOkB
PAGE 1 JOkB
PAGE 0 JUkB
WQRKSPACE
BOOT
SCRATCH BLOCK
STACK
VECTORS
I PHYSICAL M£:I.lORY
I...., ~
I
"\
1\
I~~ I~~ ~
'tDIORY :'>tA:-;'AGEME;IIT
226
VIRTl.'AL I 'tDICRY
177777
160000
140000
120000
1000DD
060000
040000
020000
000000
Figure C2.
Subroutine organisation
FILE HANDLING
ACQUISITION
USER I/O
& STORAGE I--~ ROUTINES
TEST PROGRAMS.
127
CONNECT TO
HOST
SEND DATA TO HOST
DISPLAY ROUTINES
FLOATING POINT
SCALING ROUTINES
