The Study About Stopping Distance of Vehicles

Intenational Jounal of Infomation Engineeing and Applications 018; 1(1): 18- http://www.aascit.og/jounal/infomation The Study About Stopping Distance of Vehicles Zhao Chun-xue School of Mathematics and Statistics, Anyang Nomal Univesity, Anyang, China Email addess Citation Zhao Chun-xue. The Study About Stopping Distance of Vehicles. Intenational Jounal of Infomation Engineeing and Applications. Vol. 1, No. 1, 018, pp. 18-. Received: Januay 1, 018; Accepted: Febuay 3, 018; Published: Mach, 018 Abstact: With the suge in the numbe of moto vehicles and pivate cas, uban oad taffic pessue inceases, and ea end collision accidents ae inceasing day by day. The implementation of the "two seconds" ule and keeping the safety ca distance can be effective in peventing the occuence of ea end collision event. In this pape, we mainly study "two seconds" ule in nomal diving conditions though establishing coesponding mathematical model. Results show the "second" law is quite applicable to actual when the vehicle speed is lowe than 36 m/s, which povides theoy basis fo the taffic studies. Keywods: Mathematical Modeling, Vehicle Stopping Distance, "Two Seconds" Rule 1. Intoduction With the apid economic development, taffic conditions and impovement of automobile consumption envionment, ca owneship has inceased damatically. The gowing tension between the gowing demand fo tanspotation and existing tanspotation facilities is becoming moe and moe seious, such as taffic congestion, taffic safety and enegy waste. Taffic safety, as an impotant facto in tanspotation, has got a lot of attention. It is an impotant task fo the cuent tanspotation system to pevent and educe taffic accidents and ensue the smooth and safe oad taffic. A lage numbe of studies show that educing speed and inceasing the distance of wokshop can effectively pevent and educe the occuence of taffic accidents. Fo example, Niu et al. [1] eseached on ca-following distance detection system of bus based on CCD camea technology; Wende et al. [] collected a lage numbe of ca shape infomation as matching template database of image ecognition, compaed the image of the detected ca with the template in the database, obtained the pefomance data of the font ca, and then made a easonable judgment about the elationship between the fowad vehicle and the ca; Huang et al. [3], [4] poposed the two-dimension econstuction algoithm and distance measuement algoithm based on the single-ocula vision. Zhao et al. [5], [6], [7] intoduced the pocess of applying monocula vision technology to the acquisition of multiple infomation of the fowad vehicle, used the symmety measue to detect the pesence of the fowad vehicle, and estimated the tacking taget. Zhang et al. [8], [9] analyzed the spacing of stable ca-following state and the ca-following state of acceleation and deceleation; Zheng et al. [10] studied the safety diving distance of diffeent ca-following states in highway. Xia et al. [11] studied the influence of vehicle spacing on load effect. Kui et al. [1] discussed the effect of lateal wind and longitudinal spacing on the two tucks in tandem. Gao et al. [13] studied the adaptive cuise contol aimed to achieving the contol fo maintaining safe inte-vehicle distance. Jiang et al. [14] established a mathematical model of ea-end collisions though the calculation of distances taveled by the font vehicle and the ea in diffeent phases of the baking pocess afte the bake lamp of the font vehicle lights. Zhai et al. [15] studied the feedback contol of a class of coupled-map fuzzy time-delay ca-following system. Ning et al. [16] built a model based on intelligent contol of vehicle following distance. At pesent, all kinds of algoithms have thei advantages and disadvantages, but thee is vey little eseach based on the two-second ule. The "two-second" ule poposes it is necessay to popely incease the spacing of the wokshops. The "two-second" ule can pevent collision cashes by maintaining pope safety ca spacing. On the oad, the dive can choose a fixed content of the oad fo efeence, the font ca passed though the fixed efeence of the oad, the afte dive stats eading seconds, "fo a second, two seconds," if counted, the afte ca did not aive at the efeence object, which explains it is safe and suitable fo distance. On the othe hand, if the dive does not count a couple of seconds, the vehicle has eached the efeence, which explains the gap

Intenational Jounal of Infomation Engineeing and Applications 018; 1(1): 18-19 between the two cas is not safe enough, it should slow down immediately. Theefoe, the time inteval between the font ca and the afte ca passing though this efeence is moe than two seconds, then the distance is suitable. It is the so-called "two second" ule. Based on the two-second ule, we establish a model to veify the validity of the two-second ule in the pape.. Models.1. Model Analysis Assuming that ca total stopping distance L is divided into eaction distance L and baking distance L b. The eaction distance is the diving distance fom the dive awae of paking time to eally stat baking vehicle moment; The baking distance is the sliding distance fom the moment when the dive stats baking to the moment the vehicle stops. That is L = L + L We fist study the eaction distance L. To simplify the opeation, assuming L is influenced by eaction time t and speed v, that is, b L = f ( t, v) The eaction time t is affected by dive's pesonal diving factos, vehicle opeating system factos, taffic envionment and natual weathe [11]. When the dive bakes, the vehicle opeating system needs coesponding time, it is called the system time, which is defined the time elapsed fom the dive contacts the bake pedal to the bake. Howeve, the system time is elatively negligible to moden vehicles because the ole of the system time is vey small elative to the people themselves. the dive's eaction time depends on the sensitive degee of unexpected cicumstances, the instinct of the eflection and visibility etc. In the pape, we study its geneal ule, so we take the mean values of the above vaiables. In the model, the mean value of detail factos is chosen. At the same time, we choose geneal moto vehicle speed and vehicle length. Assume that a dive's eaction time is nomal, and thee ae not any accident happened in the pocess of baking. Then we discuss the baking distance L b. The diving speed of the vehicle and its own quality ae impotant factos in the study of baking distance. In actual diving, of couse, it is necessay to conside the baking efficiency of the vehicle, the type and state of the tie, the oad condition and the weathe conditions at that time. In the pape the effects of the factos ae also ignoed, and assume the aveage condition of the factos is satisfied. So in the sub-model, we assume that Lb is a function of the quality mand speed v of the vehicle. That is L = h( m, v).. Build Models and Tests b Fo the eaction distance, suppose the vehicle is taveling at a constant speed at the time inteval fom that the dive is detemined to stop until the baking action, the vehicle is taveling at a constant speed, namely the esponse distance L is the poduct of eaction time t and velocity v: L = T v (1) To veify the ationality of the eaction distance model, we use the data about the actual obseved distance and baking distance of the dive that the U.S. highway administation povides on table 1, and give the elation gaph about eaction distance and speed as shown in figue 1, the dive's eaction distance is popotional to the speed. The popotional elationship is as follows: L = 0.75 v () Table 1. The eaction distance and baking distance obseved. v(m/s) L (m) L b(m) L(m) Obsevations Aveage Obsevations Aveage 9 7 5-7 (6) 1-13 (1.5) 11 9 8-10 (9) 16-18 (17) 13 10 11-14 (1.5) 1-4 (.5) 16 1 14-18 (16) 6-30 (8) 18 13 0-4 () 33-38 (35.5) 0 15 5-31 (8) 40-47 (43.5) 17 3-40 (36) 49-57 (53) 5 19 40-50 (45) 59-69 (64) 7 0 49-6 (55.5) 69-8 (75.5) 9 60-75 (67.5) 8-97 (89.5) 31 3 7-90 (81) 96-113 (104.5) 34 5 86-107 (96.5) 11-133 (1.5) 36 7 10-17 (114.5) 17-154 (140.5) Thee may be the coesponding eo between the esult and the actual situation. In this pape we assume it is an ideal situation.

0 Zhao Chun-xue: The Study About Stopping Distance of Vehicles v (m/s ) L b (m) Obsevations Aveage 841 60-75 (67.5) 961 7-90 (81) 1156 86-107 (96.5) 196 10-17 (114.5) Based on table, the elation gaph about baking distance and speed squaed is shown in figue, the image is a staight line though the oigin. Especially at lowe speed, the atio between the baking distance and the speed squaed is moe obvious, which veifies the ationality of ou hypothesis. The popotional elationship is as follows: Lb = 0.08V (6) Figue 1. The elationship between the eaction distance and the speed. Then we can get k = 0.08. At a highe speed, howeve, the atio needs to be futhe tested. Fo the baking distance, we assume that the maximum baking foce F is used duing the baking pocess. The wok duing the baking distance taveled L b unde the action of the maximum baking foce F is FL b. Duing the pocess, the speed of the vehicle is changed fom V being to0. Fom the law of consevation of enegy, the change in kinetic enegy is equal to the wok done by the maximum baking foce in the baking pocess, namely: FLb 1 = mv (3) In addition, when the maximum baking foce F is applied to the vehicle, the maximum acceleation of the vehicle a is fixed. Theefoe, fom the Newton's second law, we can get F = ma (4) Fom (3) and (4), the following popotions ae obtained: b (5) L V In this pape, we assume Lb = kv. Then we use the data in table 1 to test the equation (5) and get the value of k. To veify the ationality of the baking distance model, based on table 1, we give the value of baking distance and speed squaed in table. Table. The speed squaed v and baking distance L b. v (m/s ) L b (m) Obsevations Aveage 81 5-7 (6) 11 8-10 (9) 169 11-14 (1.5) 54 14-18 (16) 34 0-4 () 400 5-31 (8) 44 3-40 (36) 65 40-50 (45) 79 49-6 (55.5) Figue. The elationship between the baking distance and the speed squaed. Fom fomula () and (6), we can get the ca total stopping distance L as follows: = 0.75 + 0.08 (7) L V V To veify the ationality of the the ca total stopping distance, based on table 1, we give the mean value of the obseved data fom the total stop distance of the vehicle L and the pedicted data fom the model (7) Obsevation L in table 3. Pediction Table 3. The speed total distance obseved L obsevation and total distance pedicted L Pediction. speed (m/s) L obsevation (m) L Pediction (m) 9 1.5 13.3 11 16.5 17.93 13.5 3.7 16 8 3.48 18 35.5 39.4 0 43.5 47 53 55. 5 64 68.75 7 75.5 78.57

Intenational Jounal of Infomation Engineeing and Applications 018; 1(1): 18-1 speed (m/s) L obsevation (m) L Pediction (m) 9 89.5 89.03 31 104.5 100.13 34 1.5 117.98 36 140.5 130.6 Conside the oughness of the data mentioned in the hypothesis and the incomplete accuacy of the data, and the esult is shown in figue 3 accoding to table 3, we can get, when the vehicle speed is less than o equal to 36 m/s, LObsevation and L Pediction ae consistent, which indicates the feasibility of the model. Howeve, when the vehicle speed exceeds 36 m/s, the total stopping distance of the vehicle pedicted is significantly undeestimated. It emains to be seen. but the speed of the vehicle exceeds 36 m/s, the "two-second" ule geatly undestates the total stopping distance of the vehicle. In futue eseach, moe influential factos need to be consideed duing the pocess of building the model. Acknowledgements The eseach was suppoted by National Natual Science Foundation of China (7117114, 11401011), it was also suppoted by Natual Science Reseach Poject of the Education Depatment in Henan Povince (14B11003) and Reseach Development Poject of Anyang Nomal Univesity (AYNU-KP-A0). Refeences [1] Niu Shi-feng, Li Li, Ren Chao-wei, Reseach on ca-following distance detection system of bus based on CCD camea technology, Science Technology and Engineeing, 016, 16 (11): 198-0. [] Wende s., Dietmaye K., 3D vehicle detection using a lases scanne and video camea, IET Intelligent Tanspot Systems, 008, (): 105-11. [3] Huang Xi-yue, Cai Yi, Road test in intelligent assistant opeating system fo automobile safety, Jounal of Chongqing Univesity: Natual Science Edition, 000, 3 (): 6-30. [4] Huang Xi-yue, Cai Yi, Detection of obstacles in the intelligent assistant opeation system of automobile, Jounal of Chongqing Univesity: Natual Science Edition, 000, 3 (4): 13-16. Figue 3. The ca total stopping distance. 3. Model Applicability Analysis Based on analysis and inspection of the eaction distance, baking distance and total stop distance fo the dive, it can be found that the vehicle speed is lowe than 36 m/s, the "second" law is quite applicable to actual; When the speed of the vehicle exceeds 36 m/s, the "two-second" ule geatly undestates the total stopping distance of the vehicle because we lowe estimate the vehicle stop distance duing the pocess of solving the dive eaction distance and baking distance befoe the vehicle speed eaches 36 m/s. Afte that, we also oveestimated the stopping distance of the vehicle. In addition, we ignoe a lot of influence of natual and human factos in the model, such as individual dives diving conditions, bakes, oad pavement condition and visibility of gavity, etc., which povides a diection fo futue eseach on taffic safety issues. 4. Conclusions In this wok, we study the applicability of the "second" law though building the model of the eaction distance, baking distance and total stop distance. Results show the "second" law is quite applicable to actual when the vehicle speed is low, [5] Zhao Feng, Zhao Rongchun, Application of split one meging method in image segmentation and object extaction, Jounal of Nothwesten Polytechnical Univesity, 000, 18 (1): 116-10. [6] He Yousong, Wu Wei, Chen Mo, et al. Vehicle image ecognition study based on bag of featues, Video Engineeing, 009, 33 (1): 104-107. [7] Zhou Tao, Zhang Jiye, Vehicle detection and ecognition of video image, Compute engineeing and applications, 011, 47 (19): 166-169. [8] Zhang Zhi-yong, Huang Yi, Ren Fu-tian, Analysis method of distance headway in ca following behavioal at steady egime, Jounal of Beijing univesity of technology, 010, 36 (): 19-. [9] Zhang Zhi-yong, Huang Yi, Ren Fu-tian, Reseach of distance headway ca following behavioal at acceleation/deceleation egime, Jounal of Beijing univesity of technology, 009, 35 (6): 775-779. [10] Zheng An-wen, Zhang Bing-huan, Safety distance unde diffeent following states on expessway, Jounal of Wuhan univesity of science and technology (Natual science edition), 003, 6 (1): 54-57. [11] Xia Zhang-hua, Chen Jun-min, Zong Zhou-hong, Lin You-qin, Vehicle load effect of expessway bidge in the state of lanes meging, Jounal of Chang an Univesity (Natual science edition), 017, 37 (1): 76-84.

Zhao Chun-xue: The Study About Stopping Distance of Vehicles [1] Kui Hai-lin, Xu Xiang-gang, Li ming-da, Tian Chong-he, Effect of lateal wind and longitudinal spacing on the two tucks in tandem, Jounal of Jilin Univesity (Engineeing and technology edition), 016, 46 (5): 146-1431. [13] Gao Zhen-hai, Yan Wei, Li Hong-jian, Hu Zhen-cheng, A vehicle adaptive cuise contol algoithm based on simulating dive s multi-objective decision making, Automotive Engineeing, 015, 37 (6): 667-673. [15] Zhai Cong, Liu Wei-ming, Tan Fei-gang, Feedback contol of a class of coupled-map fuzzy time-delay ca-following system, Jounal of South China Univesity of Technology (Natual science edition), 017, 45 (1): 9-17. [16] Ning You-jiang, Zhao Jin, Zhang Bing-kun, Shi Qing, Simulation based on intelligent contol of vehicle following distance, Compute Simulation, 017, 34 (9): 146-150. [14] Jiang Qing-biao, Fu Yun-fa, Reseach on ea-end collision, Natual Science Jounal of Xiangtan Univesity, 016, 38 (3): 74-77.