3rd International Conference on Civil, Transport and Environment Engineering (ICCTEE'2013)Dec. 25-26, 2013 Bangkok (Thailand)
Novel Method of Determining Braking
Distance of Heavy Vehicle using Advanced
Simulation Technique
Airul Sharizlia, Rahizar Ramlib, Mohamed Rehan Karimc, Ahmad Saifizulc
streams may reach 20% of all traffic on the road (depending
on locations). Since heavy vehicles vary in types and sizes, the
vehicle’s gross vehicle weight (GVW) would vary
considerably especially when loaded. The situation would be
more serious when truck overloading exists on the roads.
An analysis of traffic accidents indicates that human factor
largely contributes to road traffic accidents [3]. Human factor
involved in heavy vehicle crashes can be subdivided into
various forms. The most common critical error made by
drivers, whether they are truck drivers or other involved
drivers, appears to be misjudgement of the safe distance gap,
which is due to drivers following too closely to the leading
vehicle and are over confident in their ability to stop the truck
before it crashes [4]. Most drivers consider themselves above
average in terms of driving skill. A number of studies
conducted in various countries around the world demonstrate
that up to 90% of drivers think they are an above average,
low-risk driver [5]. For that reason, drivers believe they can
travel above the speed limit and not place themselves at high
risk.
Vehicle weight is one of the essential parameters in vehicle
design study that can affect vehicle driving, braking and
handling performance characteristics [6] and most of the time,
vehicle dynamics influence the drivers’ behaviour when
controlling their vehicles [7]. The study by Saifizul et. al. [8,
9] has shown that the GVW for heavy vehicles has a direct
influence on speed whether the vehicle travels in a vehicle
following situation or in free flow condition.
Issue in Current Theoretical Formulation and Software
Calculator for Braking Distance
Braking distance (BD) is the distance taken for a vehicle to
stop from a specific speed without considering the driver’s
reaction time. The ability of a vehicle to achieve short braking
distance under variables of speed and load is an essential
aspect of heavy vehicle (HV) safety. In literature, there were
several theoretical formulation and software calculator
conventionally used in BD calculation [10, 11, 12]. There are
a few theoretical formula that relate the braking distance with
vehicle loading such described in reference [13].
Unfortunately, the formula is too complicated and complex for
quick calculation. There were few calculator was introduced to
calculate the braking distance or stopping distance such as in
reference [14]. One observation made regarding the parameter
considered in most of these calculators for BD is that, the
calculators assume the BD is independent of vehicle mass and
Abstract— One of the main causes of fatal vehicle crashes is
attributed to the failure of a vehicle to decelerate and stop without
hitting the leading vehicle or any other object when applying the
emergency brakes due to unforeseen circumstances. Thus, a better
understanding of the characteristics of a vehicle’s braking
performance is crucial in developing a reliable intelligent collision
avoidance system and in creating safety awareness among vehicle
drivers. Changes in the vehicle dynamics’ characteristics such as
vehicle weight, travel speed and vehicle classification will affect the
vehicle’s braking performance and its ability to stop safely in an
emergency situation. As such, the aim of this study is to establish a
more realistic braking distance model for various classifications of
vehicles under various loads and travel speed. These main vehicle
parameters which have not been explicitly considered in previous
braking distance analytical models are included in the analysis and
followed by the proposed regression model. This study uses a kind of
complex virtual prototyping software to simulate vehicle dynamics
and its braking performance characteristics. The commercial multibody dynamic simulation was used to generate braking distance data
for various heavy vehicle classes under various loads and speed
conditions. Using non-linear regression analysis to the simulation
results, a mathematical expression has been established. In addition, a
graphical user interface (GUI) braking distance calculator was
developed based on the regression model. It is envisaged that this
calculator would provide a more realistic depiction of the real
situation for safety analysis involving heavy vehicles.
Keywords—Braking Distance, Gross Vehicle Weight (GVW),
Vehicle Classification, Heavy Vehicle, Road Safety
I. INTRODUCTION
T
HE number of road accidents occurred in developing
countries such as Malaysia over the past decade, showed
worrying trends. The number of road accidents in Malaysia
increased by 59% from 250,429 cases in 2000 to 397,194
cases in 2009 [1]. From this figure, 14% (55,607) of the
accidents occurred involved heavy vehicles such as bus, lorry
and trailer/tanker [2]. Although the number of registered
heavy vehicles hardly makes up 5% of total vehicle
registrations, the composition of heavy vehicles in traffic
a
Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur,
Malaysia; (e-mail: [email protected]).
b
Advanced Computational and Applied Mechanics (ACAM), Faculty of
Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia (e-mail:
[email protected]).
c
Center for Transportation Research (CTR), Faculty of Engineering,
University of Malaya, 50603, Kuala Lumpur, Malaysia (e-mail:
[email protected] ; [email protected]).
48
3rd International Conference on Civil, Transport and Environment Engineering (ICCTEE'2013)Dec. 25-26, 2013 Bangkok (Thailand)
vehicle classification hence only consider the speed of the
vehicle. The characteristics of these two important HV
parameters are assumed to be the same for all types of
vehicles.
The impetus for these studies arises from the intrinsic
interest in understanding the factors which influence the BD of
HV, from the fact that there was no detail investigation that
relates the BD as a function of GVW and vehicle
classification. This study has a twofold objective. The first
objective is to establish the regression model of the BD which
incorporates the GVW and vehicle classification. The second
objective is to develop a user friendly graphical user interface
(GUI) braking distance calculator. This calculator is designed
to give an accurate projection of heavy vehicle braking
distance based on regression model from the first objective.
starting from 40km/h with 10km/h intervals until 100km/h.
The entire simulations at the selected velocities are repeated
for different GVWs. This is followed by simulations for the
different vehicle types i.e. 3-axle SUT and 4-axle SUT.
III. RESULT AND DISCUSSION
In this paper, numerical data were generated as described
in previous section. A total of 232 data were generated
throughout the simulations. The HV simulation data were
grouped according to GVW, vehicle classification, and
speed for analysis and line graph were plotted as shown in
Figure 1.
TABLE I
UNITS FOR MAGNETIC PROPERTIES
Items
Details
Analysis mode
Road condition
Starting velocity
II. METHODOLOGY
The brake performance of vehicles can be analysed in
several ways. This can be done through an actual experimental
method or through advanced computer simulation. Obviously,
the process of building and instrumenting the prototype for
actual experimental testing involves significant engineering
time and expenses. With the evolution of computer science,
computer simulation offers a better alternative to understand
physical problems with the capability to emulate extreme
conditions and complex engineering analysis. These
techniques are often used as an alternative to very costly
experimental methods. In this study, MSC.ADAMS software
was used to generate BD data for two to four axle single unit
truck (SUT) under various GVW and speed conditions.
There are three main steps involved in obtaining the BD
data from MSC.ADAMS/Truck which are (a) Virtual Vehicle
Modelling, (b) Simulation and (c) Data generation and
interpretation. Since the aim of the study is to develop a model
that can reflect an actual two to four axle BD situation, it is
important to develop a more realistic SUT models. Thus, in
this study, the vehicle model and its specification for SUT 2axle, 3-axle and 4-axle have been developed in accordance to
vehicle class available on the Malaysian roads. All of these
SUTs will be reconfigured according to the existing SUTs’
parameters.
Simulation was carried out under the assumption that the
vehicle has reached a steady state condition and maintains
constant forward velocity before the brakes are applied at
285N. The braking analysis and tire properties to run this
simulation are shown in Table 1 and Table 2. Furthermore, air
drum brake and parabolic leaf spring suspension are used for
the heavy vehicle subsystems which are typically used in
Malaysia. For this study, a straight and flat road profile is
employed whereby differences in road materials and stiffness
are not significant.
As stated in the objectives for this study, GVW is the
crucial element for this simulation. The lump mass added in
storage compartment will be assigned with different mass
(5000Kg interval) for each simulation. The GVW is calculated
when appropriate loading is assigned for the heavy vehicle.
The whole event is conducted under constant forward velocity
Braking
Dry, Straight road
30 km/h to 100 km/h with 10km/h
interval
At 5 second
285N
0.2 second
Time start to brake
Brake force
Reaction time
TABLE II
THE TIRE PROPERTIES
Items
Unloaded Radius
Width
Aspect Ratio
Vertical Stiffness
Vertical Damping
Rolling Resistance
49
Value
507 mm
304.8 mm
0.45
873 N/mm
10 Ns/mm
3.0
3rd International Conference on Civil, Transport and Environment Engineering (ICCTEE'2013)Dec. 25-26, 2013 Bangkok (Thailand)
TABLE III
REGRESSION COEFFICIENTS WITH P-VALUE OF A AND B
Vehicle
type
Speed
,v
30
0.091
0.001
0.169
0.002
7.149
0.001
0.977
<0.001
12.521
<0.001
0.992
60
0.385
0.001
16.650
<0.001
0.986
70
0.499
0.004
23.743
0.001
0.954
80
0.630
0.006
31.840
0.001
0.942
N
5
90
0.804
0.005
40.042
0.001
0.948
100
0.450
0.007
51.104
0.001
0.934
30
0.115
0.001
2.559
<0.001
0.957
40
0.207
<0.001
4.536
<0.001
0.988
50
0.330
<0.001
7.3
<0.001
0.988
60
0.477
<0.001
10.731
<0.001
0.987
70
0.649
<0.001
14.83
<0.001
0.986
80
0.851
<0.001
19.591
<0.001
0.987
90
1.080
<0.001
24.834
<0.001
0.986
100
1.335
<0.001
30.695
<0.001
0.986
30
0.130
<0.001
1.736
0.003
0.961
40
0.269
<0.001
2.013
0.014
0.985
50
0.427
<0.001
3.255
0.019
0.982
6
60
0.620
<0.001
4.834
0.023
0.979
70
0.853
<0.001
6.451
0.031
0.976
80
1.090
<0.001
9.764
0.028
0.969
90
1.415
<0.001
11.03
0.027
0.977
100
1.750
<0.001
13.592
0.03
0.975
Fig. 1 Effect of GVW on BD of Heavy Vehicle at Different Speeds
7
TABLE IV
REGRESSION COEFFICIENTS WITH P-VALUE FOR CI
Based on plots in Figure 1, a BD regression model for every Vehicle
category of heavy vehicle can be proposed. The proposed type
2
model incorporating GVWs and travel speeds of HVs can be AXLE
expressed as follows:
(p-
Where BDt is a braking distance for HV in meter, w is
GVW and v is speed. The first regression calculation was done
to determine coefficients of the regression lines, a and b in
Equation (1) for various speed. The value of these coefficients
and coefficients of determination, R2, for all cases are
described in Table 3. Another regression calculation was done
to determine the coefficients of the regression lines, Ci where
i=1, 2, 3 and 4 in Equation (1) and coefficients of
determination, R2 for all cases are described in Table IV.
R2
0.966
0.237
4 axle
Where
3.891
p-value
(b)
40
3 axle
(1)
0.002
b
(consta
nt)
50
2 axle
BD t = aw + b
a = C1v + C2
b = C3v + C4
a
p-value
(a)
value)
3
AXLE
(pvalue)
4
AXLE
(pvalue)
C1
C2
C3
C4
19.966
0.008
-0.132
0.667
0.008
0.401
<0.001
0.017
-0.502
0.404
0.001
11.880
<0.001
0.023
0.001
-0.674
<0.001
0.178
0.001
-4.620
<0.001
<0.001
<0.001
0.002
R2(a)
R2(b)
N(a)
0.719
0.970
8
0.977
0.976
8
0.977
0.964
8
N(b)
Using Equation (1), the respective values of BD can be
determined for the different vehicle types and GVW at various
speeds. The proposed model for BD as a function of GVW for
different classes of vehicle has been derived as shown in Table
5. Based on this table, a user friendly GUI Braking Distance
calculator was developed as shown in Figure 2.
50
8
8
8
3rd International Conference on Civil, Transport and Environment Engineering (ICCTEE'2013)Dec. 25-26, 2013 Bangkok (Thailand)
TABLE V
PROPOSED MODEL FOR BRAKING DISTANCE (BD)
Vehicle Type
Braking Distance Model
2 Axle
0.008Vw - 0.132w+0.667V-19.299
3 Axle
0.017Vw - 0.502w+0.404V-11.880
4 Axle
0.023Vw - 0.674w+0.178V-4.620
[10]
[11]
[12]
[13]
[14]
Fig. 2 Braking Distance Calculator
IV. CONCLUSION
This study aims to propose a regression model for braking
distance that not only considers speed but also two others
important parameters that is gross vehicle weight (GVW) and
Vehicle Classification. From this regression model, a novel
BD calculator was developed to offer more precise and easy to
use for predicting and analysing braking distance.
There are two major outcomes form these studies. First
outcome is a development of a new regression model for
braking distance that integrates three important factors that is
speed, gross vehicle weight and vehicle classification. The
second outcome is a development of a new user friendly GUI
calculator for braking distance based on the new model.
ACKNOWLEDGMENT
The authors would like to acknowledge the assistance from
the flagship grant FL020-2012 awarded by the University of
Malaya.
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http://www.csgnetwork.com/stopdistcalc.html