# Minimum Safety Distance Model of Vehicle Under the Influence of Two Factors

DOI : 10.17577/IJERTV7IS090030

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#### 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 re-derived 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 words-Minimum 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, rear-end collisions account for about 14%, which is a high-incidence accident. If the distance between cars can be calculated more accurately, rear-end 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 anti-collision 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 4-input 1-output mode.

1. 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 1-4 lists the effects of various influencing factors on the reaction time.

Table 1 Effect of age on reaction time

 age Range Mean variance 18-35 1.02-1.8 1.36 0.23 35-55 0.94-2.27 1.89 0.21 55-70 1.5-2.65 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

2. Output of fuzzy reasoning

age

Pre-fatigue reaction time

Reaction time after fatigue

18-35 0.92-1.03 1.68-1.74

35-55 1.06-1.22 2.17-2.32

55-70 1.05-1.37 2.35-2.58

Table 3 Effect of driving age on reaction time

 Driving Driver response Mean variance age time Figure 3 driver reaction time membership function 0-10 0.97-1.39 1.27 0.25 10-30 1.01-1.33 1.19 0.36 The driver response time can be determined by the four

Over30 0.83-1.26 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

 0-0.3 1.32-1.45 1.37 0.31 0.3-0.7 1.17-1.30 1.26 0.27

0.7-1 0.97-1.25 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, middle-aged n2, and old-aged n3. In the membership function

membership function is used. The membership function of the driver response time is shown in Figure 3.

3. Fuzzy rule

In this paper, the model of 4-input and 1-output 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 three-dimensional relationship diagram

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 three-dimensional relationship between input and output

Deduced

F

Xb max

mg

3

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

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

1. 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

1. Front car non-uniform 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

1. 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

taken to overcome the gap of the braking system are same.This paper sets t value range 0.05-0.1 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

deceleration to the maximum of the brake deceleration.The

not reached 150 meters.

value range of this paper

2

t is set to 0.15-0.3 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 7-10.

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 rear-end collision accidents, and it is superior to the traditional model in improving road traffic efficiency.

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