 Open Access
 Total Downloads : 0
 Authors : Zhang Yu , Guan Zhiwei
 Paper ID : IJERTV7IS090030
 Volume & Issue : Volume 07, Issue 09 (September – 2018)
 Published (First Online): 05012019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Minimum Safety Distance Model of Vehicle Under the Influence of Two Factors
Minimum Safety Distance Model of Vehicle Under the Influence of Two Factors
Zhang Yu
School of Automotive and Transportation Tianjin University of Technology and Education Tianjin, China
Guan Zhiwei
School of Automotive and Transportation Tianjin University of Technology and Education Tianjin, China
Abstract In the traditional safety distance model, a single factor, such as driver response time or road surface adhesion coefficient, is generally considered. In fact, the safety distance is determined by many factors. Considering the single factor, the safety distance is different from the actual one. Based on previous studies, considering the two factors of driver response time and road adhesion coefficient, the calculation
. ANALYSIS OF THE BRAKING PROCESS
Under normal circumstances, when the car is bumping in front of the road while driving normally, it is assumed that the speed of the car movement is v , the unit is km / h , and the maximum braking deceleration during
formula of safety distance is rederived and modeled, and the driver
braking is ab
and the braking phase is for the four stages
response time is fuzzy inferred by MATLAB. The final model is verified, and a more accurate minimum safety distance is obtained, which has certain reference significance for studying the fluency of traffic flow.
Key wordsMinimum Safety Distance; Driver Response Time; Road Surface Adhesion Coefficient; Fuzzy Reasoning
of 1 2 3 4
[3]. As shown in figure 1:At present, China's car ownership is increasing, and it also brings frequent traffic accidents. According to statistics, in China's traffic accidents, rearend collisions account for about 14%, which is a highincidence accident. If the distance between cars can be calculated more accurately, rearend collisions may be greatly reduced.In the
Figure 1 Automotive Braking Process
intelligent auxiliary driving system, the maintenance of the safe distance is extremely important. The distance can
1 is called driver response time. 2
is called the
ensure that the vehicle is relatively safe from the front vehicle during longitudinal driving. All along, scholars have studied the safety distance of the workshop, such as the
brake action time.
3 is called continuous braking time [4].
safety distance model based on the headway distance [1], the vehicle anticollision safety distance model [2], etc. These
The time
4 takes for the driver to release the brake pedal.
methods can determine the distance between the two vehicles to some extent. The safety car spacing, which is generally a fixed value. However, there are many shortcomings in practical applications. For example, the change of the driver or the ground adhesion coefficient will affect the driving distance of the vehicle during braking,thus
In summary, it can be seen that in the normal driving process, considering the driver's reaction time, the distance traveled from the obstacle in front of the vehicle to the time
of complete stop is
a
2
changing the safety distance. This paper will add the driver
'
v2
s s1 s2 s3 v1 v 2
2a
2
v ''
2
''

b 2
24
1
in combination with the results of previous research. The reaction time and the adhesion coefficient of different road surfaces optimize the model of the vehicle spacing, and finally obtain the safety distance model of different types of drivers when driving on different roads with different adhesion coefficients.
.The Key Project of Tianjin Natural Science Foundation of China (Grant No. 16JCZDJC38200)
Tianjin Science and Technology Innovation Platform Project
16PTGCCX00150
b
. RIVER RESPONSE TIME DETERMINATION
In normal driving behavior, the time during the driver finds the obstacle in front to start braking is called the driver reaction time. There are several situations that affect the driver's reaction time: age and gender, the degree of urgency of the obstacle, the presence or absence of fatigue
driving, the influence of alcohol or drugs on the driver, the driver's driving mood, and the driver's skill[5].
These factors are qualitative descriptions of driver response time, which is difficult to quantify, so this paper uses fuzzy reasoning to determine the driver's reaction time. In a series of surveys and measurements, the driver's reaction time is between 0.5 and 3 seconds [6], which has a greater impact on the braking distance of the vehicle at high speeds. In this paper, MTALAB is used to perform fuzzy inference on driver response time with a 4input 1output mode.

Input of fuzzy reasoning
The four inputs in this paper are the driver's age, driver's driving experience, driver's fatigue level and the degree of urgency of the obstacles in front. Through the driving simulator experiment, Table 14 lists the effects of various influencing factors on the reaction time.
Table 1 Effect of age on reaction time
age
Range
Mean
variance
1835
1.021.8
1.36
0.23
3555
0.942.27
1.89
0.21
5570
1.52.65
2.31
0.27
Table 2 Effect of fatigue on reaction time
of the obstacles, the degree of urgency of the obstacles is divided into ten levels, that is, the domain is [0, 1], which is divided into slow speed z1, moderate speed z2, and fast speed z3. In the membership function of fatigue degree, fatigue is divided into ten grades, that is, the domain is [0,10]. Because the degree of fatigue is related to human physiological factors, it is a nonlinear relationship, so Gaussian function is adopted. It is divided into three fuzzy sets with low fatigue degree p1, moderate fatigue degree p2, and high fatigue degree p3. The corresponding membership function is shown in Figure 2.
Figure 2 Membership Function Of Four Fuzzy Inputs

Output of fuzzy reasoning
age
Prefatigue reaction time
Reaction time after fatigue
1835 0.921.03 1.681.74
3555 1.061.22 2.172.32
5570 1.051.37 2.352.58
Table 3 Effect of driving age on reaction time
Driving
Driver response
Mean variance
age time Figure 3 driver reaction time membership function
010
0.971.39
1.27
0.25
1030
1.011.33
1.19
0.36
The driver response time can be determined by the four
Over30 0.831.26 1.04 0.29
Table 4 Effect of obstacles on reaction time
The degree of
Driver
factors age, driving age, fatigue level and the degree of urgency of obstacles. The driver response time is within [0.5, 3] and is divided into five ranges, which are Fastest T1. Faster
urgency of the
response time
Mean variance
T2, moderate T3, slower T4, slowest T5. A Gaussian
obstacle
00.3
1.321.45
1.37
0.31
0.30.7
1.171.30
1.26
0.27
0.71 0.971.25 1.01 0.26
In the membership function of driving age, the domain is [0, 50] , which can be divided into low driving age j1, middle
driving age j2, and high driving age j3. In the membership function of age, the domain is [18,70], divided into youth n1, middleaged n2, and oldaged n3. In the membership function
membership function is used. The membership function of the driver response time is shown in Figure 3.

Fuzzy rule
In this paper, the model of 4input and 1output is adopted. The and connection between different variables is used. The four variables in this paper have three fuzzy sets for each variable, so the corresponding fuzzy rules have
3 3 3 3 81rules, as shown in Table 5.
factor
n1j1
n1j2
n1j3
n2j1
n2j2
n2j3
n3j1
n3j2
n3j3
Peak
Sliding
Maximum
p1z1
T2
T1
T1
T2
T2
T1
T3
T2
T2
pavement
adhesion
adhesion
brake
deceleration
p1z2
T2
T2
T1
T2
T2
T1
T3
T2
T2
coefficient
coefficient
(Unit: m /s2 )
p1z3
T2
T1
T1
T1
T1
T1
T3
T2
T1
Asphalt
0.85
0.75
8.33
asphalt wet
0.6
0.5
5.88
p2z1
T3
T3
T2
T4
T4
T4
T4
T4
T4
Concrete
0.8
0.7
7.84
wet
p2z2
T3
T3
T3
T4
T3
T3
T4
T4
T4
Snow
p2z3
T4
T2
T3
T3
T3
T3
T3
T3
T3
(Press tight
0.2
0.15
1.96
ice
0.1
0.07
0.98
p3z1
T4
T4
T3
T5
T4
T5
T5
T5
T5
p3z2
T4
T3
T3
T5
T4
T5
T5
T5
T5
In an emergency, the
driver slam
s on the brakes and the
p3z3
T3
T3
T2
T4
T3
T4
T5
T4
T4
vehicle is fully braked.
Because of
the ABS,
the ground
Table 5 Driver Response Time Fuzzy Rule Table
After determining the driver's age, driving age, fatigue level, and the degree of urgency of the obstacle, the driver's reaction time can be obtained by defuzzifying in MATLAB.
Figure 4 is a threedimensional relationship diagram
Table 6 Size of the adhesion coefficient of different road SURFACES
adhesion coefficient can reach the peak adhesion coefficient, and the vehicle can generate the maximum braking deceleration. Let the maximum ground braking force of the vehicle be FXb max , the normal reaction force of the ground to
the wheel is FZ , and the road surface adhesion coefficient is :
the relationship between the three is:
between fuzzy rule input and output.
F F
2
Xb max z
The maximum braking force of the vehicle on different road surfaces is obtained by the above formula, and the braking deceleration on different road surfaces can be obtained.
Assuming that the mass of the vehicle is m , the acceleration of gravity is g ,then the maximum brake
deceleration of the vehicle during braking can be obtained.
Figure 4 is a threedimensional relationship between input and output
Deduced
F
Xb max
mg
3
. NFLUENCE OF ROAD ADHESION COEFFICIENT ON BRAKING DISTANCE
amax
FXb max g m
4
During braking, the brake deceleration directly determines the magnitude of the brake deceleration, which is caused by the friction between the tire and the ground. The amount of friction is determined by the road adhesion coefficient. This paper considers three types of pavement conditions: dry cement pavement, wet slip concrete pavement and ice and snow pavement. Table 6 lists the magnitude of the adhesion coefficient and the maximum brake deceleration for different road surfaces.
It can be known from formula (4) that
the road surface adhesion coefficient.
a
max
is related to
. ESTABLISHMENT OF A MATHEMATICAL MODEL OF MINIMUM SAFE DISTANCE
The establishment of the minimum safety distance
vehicle speed is the same.
The distance traveled by the front car is
model helps to improve the patency and efficiency of traffic
S v (t
t t ' t ' )
6
on the basis of safety. This paper mainly considers two aspects: the uniform speed of the front car and the uniform
f 2 0 1 1 2
The distance traveled by the rear car is
deceleration of the front car. Which will be discussed
S v t

v t t ' v t '



1 a
t
'
2 t '2
7
separately.
r 1 0
1 1 1
1 2 6
t
1max 2
2

Front car uniform speed
Figure 5 shows the motion of the two cars in front and
Minimum safe distance
'
S S S
d (v v )(t t t ' t ' ) 1 a
t2 t '2 d 8
rear.
1 r f 0
1 2 0 1 1 2
2
6 1max t 2 0
The meaning of each letter in the formula
v rear car speed v front car speed t to eliminate
1 2 0
the brake system clearance time t driver response time t '
1 1
the time it takes for the driver to put his foot on the brake pedal
Figure 5 Schematic diagram of vehicle movement
2
t '
deceleration of the vehicle to the same speed as the
before and after
1max
vehicle speed a the maximum brake deceleration of the
As shown in the figure, the front car runs at a constant speed, and the rear car speed is greater than that of the preceding car. In this case, if the rear car does not brake, it will collide with the preceding car at sme later time, which is
dangerous . Therefore the rear vehicle should be decelerated
when it is at a certain distance from the preceding vehicle (ie,
rear car.
The vehicle speed is the same when the brake deceleration just increases to the maximum brake deceleration.
In this case, the driving distance of the preceding vehicle is
the minimum safe distance), and decelerating to the same
S v (t
t t ' t )
9
speed as the preceding vehicle is a safe working condition.
It is assumed that the distance between the two vehicles is
f 2 0 1 1 2
The distance traveled by the rear car is
S at the beginning, and when the speed of the rear vehicle is
S v t

v t v t ' v t



1 a t 2
10
1
the same as that of the preceding vehicle, the distance traveled
r 1 0
1 1 1 1
1 2 6
1max 2
by the rear vehicle is
f
S , and the distance traveled by the
Minimum safe distance:
preceding vehicle is S ,
1 r f 0
S S S d
r
(v v )(t
t t t ) 1 a
t d
11
S
1
r
f
0
S S d
(5)
'
1 2 0 1 1 2
2
6 1max 2 0
That is, the minimum safe distance is obtained in this
2
In the formula t is the vehicle acceleration growth
paper, where
0
d is the distance between the rear and front
time.
vehicles and the speed of them are same, generally take
d0 5 m .
The front car moves at a constant speed, and the rear car speed is greater than the front one. According to the speed
The vehicles speed is the same while the brake
deceleration increases to the maximum brake deceleration and
continues to brake for a while.
In this case, the distance traveled by the preceding vehicle is
difference between the front and rear cars, it can be divided
S v (t

t t ' t

t )
12
into three situations:
When the brake deceleration is in the growth phase, the
f 2 0 1 1 2 3
The distance traveled by the rear car is
Sr
v 1 a
t 2 v2
13
Driver response time is t1 The time it takes the driver to
' 1 2
2
1
v1t0 v1t1 v1t1 v1t2 a1max t2
6
1max 2 2
2a1max
put his foot on the brake pedal is
t
'
1 Brake deceleration
Then, the minimum safe distance sought
S1 Sr S f d0
growth time is t2 Then the distance traveled by the rear
v 1 a
t 2 v2
14
' 1 2
2 ( ' )
v1 t0 t1 t1 t2
1
a1max t2
6
1max 2
2a1max
2
v2 t0 t1 t1 t2 t3 d0
car is
The time when the rear car continues to brake is
v
2
1 2
S v t v t v t ' v t 1
v t a t 2
1 2 1max 2
17
t v v 1 t
15
r 1 0
1 1 1 1
2a1max 2 24
1 2
a 2
3 2
1max
Then the minimum safe distance is

Front car nonuniform motion
S S S


d
Under such conditions, the change of the speed of the
1 r f 0
v2 v t
a t 2 v2
18
1 2
0
v t v t v t ' v t 1 1 2 1max 2 2 d
preceding vehicle becomes more and more complicated, and
the corresponding braking operation of the rear vehicle is
1 0 1 1 1 1
2a1max 2
24 2a2
based on the response of the preceding vehicle's motion state. In order to ensure that it does not collide with the preceding car, this paper considers three situations under the premise of uniform deceleration of the preceding vehicle. The motion diagram of the front car under uniform deceleration is shown
The speed of the front and rear cars is the same
This situation is similar to the previous one. Simply
change the formula (18) slightly and the minimum safe distance is:
S1 Sr S f d0
in Figure 6.
1 1 v t
a t 2
19
1
v t v t v t ' v t v2 (
0
) 1 2 1max 2 d
1 0 1 1
1 1 1 2
2a1max
2a2 2 24
Figure 6 Schematic diagram of uniform deceleration movement of the front car
The speed of the front car is greater than the speed of the
rear one .
The front car is decelerated and moved at a certain braking deceleration until it stops. In this case, the calculated minimum safety distance is the smallest. As long as the rear car and the
The speed of the front car is greater than the speed of the rear car
In this case, if the front car has been decelerating and the rear car is not processed, there will be dangerous after driving for a period of time. Therefore, the rear car should be braked to stop when the preceding vehicle speed is reduced to the same as the rear one . The distance traveled by the preceding car during this process is:
2
front car ensure this safe distance, it will not be collision and because of the small safety distance, it can also ensure the smoothness and high efficiency of traffic flow.
S f
v2
2a2
20
2
Set the front car speed is v ,The deceleration of the front
The distance traveled by the rear car is:
car is
2
a Rear car speed is
1
v The maximum brake
v2 v1
' v1t2
a t
2
1max 2
deceleration of the rear car is a , d is 5m .The displacement
Sr v1
v1t0 v1t1 v1t1 v1t2

d0
21
1max 0
a2 2 24
of the preceding vehicle from
2
v deceleration
2
a to stop is
Then the minimum safe distance is:
v2
f
S 2
16
t v2
v2 a t 2
2a2
S1 Sr S f d0 v1 (t0 t1 t )
2 2a
a 24

d0
22
' 2 2
1
2
1 1max 2
2
After the car found the front car decelerating, the time

Selection of parameters
taken to eliminate the brake system clearance is
t 0
Before the simulation, it is necessary to determine the
value of some physical quantities. From the above analysis, it can be seen that in the situation of uniform motion of the front
FIGURE 7TO10
It can be seen from figs. 7 to 8 that under the same reaction
vehicle and rear car deceleration movement, the time
0
t which
time, the influence of the road surface adhesion coefficient on
taken to overcome the gap of the braking system are same.This paper sets t value range 0.050.1 s ,the same time t '
the braking distance of the vehicle is very high. In the case of the small road surface adhesion coefficient, the maximum
0 2
from the start of the brake deceleration to the front and rear
braking distance is almost 400 meters, and the braking distance
speeds and
2
t seconds from the start of the brake
in the peak value of the road surface adhesion coefficient has
deceleration to the maximum of the brake deceleration.The
not reached 150 meters.
value range of this paper
2
t is set to 0.150.3 s
.The
As can be seen from figs. 7 and 9, while the road surface
determination of
2
t ' is related to the deceleration of the front
adhesion coefficient is same, the longer the driver reaction
and rear vehicles before and after the vehicle speed, and is analyzed in detail when doing the analysis.
.MOEL SIMULATION ANALYSIS
This paper uses the Matlab platform to simulate the model. The deceleration values of the front and rear brakes under different road adhesion factors are shown in the following table:
Table 7: Deceleration of front and rear brakes under different road surface adhesion coefficients
0.85 0.6 0.2
time is, the larger the braking distance is.
B. Front car uniform deceleration
As shown in Figure 11 to 14, in the case of uniform deceleration of the preceding vehicle, the influence of the driver's reaction time and the road surface adhesion coefficient on the braking distance of the vehicle are similar to that of the preceding vehicle. The speed range is small at the figure 12 figure 14 , because if the speed of the front car is greater than a certain value, the distance from the front car to the stop is far longer than the distance from the rear car to the speed of the deceleration, so take The range of values will be smaller.
a1max
a2
8.33 5.88 1.96
5 3 1
A. Front car uniform motion
The simulation of the front car under uniform motion is shown in Figure 710.
Figure 11to14
It can be seen from the above analysis that different driver response time and road surface adhesion coefficient have a certain degree of influence on the braking distance. In the design of intelligent auxiliary driving,different driving distances shuold be judgment and adjustment, according to different drivers and different road surface adhesion coefficients.
.CONCLUSION
In the daily driving process, different drivers have different reaction times, and different road adhesion coefficients have different braking deceleration. These two factors are important factors for calculating the safety distance through the above simulation analysis. In the case of a certain speed of front and rear vehicles, the minimum safety distance is obtained by
different drivers and different road surface adhesion coefficients is not same. If the driver's monitoring and the road adhesion coefficient are added to the intelligent auxiliary drive system, it is of great significance in preventing the occurrence of rearend collision accidents, and it is superior to the traditional model in improving road traffic efficiency.
REFERENCES
[1] Wang Jiangfeng, Shao Chunfu, Yan Xuedong, Wei Liying. Research on Minimum Safe Distance of Vehicle Lane Change Based on Virtual Reality[J].Highway transportation technology,2010,27(8):109113. [2] Luo Qiang, Xu Lunhui. Establishment and Simulation of Carfollowing odel Based on Minimum Safety Distance[J].Science and technology and engineering,2010,10(2):569573. [3] Wang Junlei, Li Baichuan, Ying Shijie, Gong Hangjun.A Study on Collision Early Warning Analysis and Minimum Vertical Safety Distance Model of Lane Change[J].Ergonomics,2004(4):1619. [4] Lu Jier, Zhu Liuhua, Zheng Rongsen, Wei Yanfang. The Impact of Driver Response Time on Traffic Safety[J].Transportation System Engineering and Information,2014,14(2):8086. [5] Critical safe distance design to improve driving safety based on vehicletovehicle communications [J] . Journal of Central South University,2013,20(11):33343344. [6] C.C.Yuan. Analysis the safety distance model and modeling DRV safety distance model[A]. IETP Associaiton.Abstract of the 2015 International Conference on Advanced Materials and Engineering Structural Technology(ICAMEST 2015)[C].IETP Associaiton:,2015:1.