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This article suggests a model for many road accidents, namely, those in which a vehicle being driven forwards encounters an obstacle such as a pedestrian, a vehicle, or a tree. An equation for speed of impact is obtained from the model. (Speed of impact is very important in determining severity of injury.) The equation is an expression in five variables. As it is elementary, it will be of interest to educators in mathematics and other subjects, as well as to road safety specialists. Two of the five variables (speed of vehicle, and distance of the obstacle) are conditions existing at the initiation of the emergency; and three are approximately termed: range of the sensing system; reaction time; and deceleration; and are properties of the system of driver and vehicle. Thus the focus is on the moment the emergency is appreciated, a few seconds before impact. The model and equation may be relevant to some railway accidents, also. In addition, the article discusses how to push our understanding to a point some seconds earlier, in the hope of throwing light on accident causation. References T. P. Hutchinson. A method of constructing models of reaction to an imminent road crash. Traf. Eng. Control 57 (2016), pp. 97–103 T. P. Hutchinson. Road Safety Theory. Published online. 2018. url: http://RoadSafetyTheory.com T. P. Hutchinson. The theory of reduction of impact speeds. Traf. Eng. Control 56 (2015), pp. 177–180 D. N. Lee. A theory of visual control of braking based on information about time-to-collision. Perception 5 (1976), pp. 437–459. doi: 10.1068/p050437 D. F. Moore. Minimization of occupant injury by optimum front-end design. Society of Automotive Engineers Technical Report No. 700416 (1970). doi: 10.4271/700416 D. Stewart, C. J. Cudworth, and J. R. Lishman. Misperception of time-to-collision by drivers in pedestrian accidents. Perception 22 (1993), pp. 1227–1244. doi: 10.1068/p221227 K. Suzuki, H. Tanaka, Y. Miichi, and M. Aga. Collision-mitigation level of collision-avoidance braking system. Int. J. Vehicle Safety 7 (2014), pp. 1–16. doi: 10.1504/IJVS.2014.058238 J. Wooller. Road traffic accidents in Adelaide and Brisbane, Australia—Excerpts from a report in preparation. Proceedings, 4th Conference, Australian Road Research Board 4 (1968), pp. 976–994. url: http://155.212.5.248/Presto/content/Detail.aspx?ctID=MjE1ZTI4YzctZjc1YS00MzQ4LTkyY2UtMDJmNTgxYjg2ZDA5&rID=OTAx&qrs=RmFsc2U=&ph=VHJ1ZQ==&bckToL=VHJ1ZQ==&rrtc=VHJ1ZQ== |
