Timothy Paul Hutchinson

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==

Regulatory testing for safety: The mathematics of broad-based results

Consider crash tests in which a car strikes a solid block. Suppose there is a particular differential equation (that includes a term in deformation to the power n) relating acceleration at any instant to deformation and velocity at that moment. If that is the case, the dependencies on impact speed of maximum acceleration, duration of impact and deformation are interconnected: the relationships are power functions, and the exponents are all determined by the exponent n in the differential equation. Data from both tests and real crashes suggest that n is about 0.5 for front wheel drive cars.

Vocational interest inventories are often designed, scored and interpreted in accordance with the six Holland types (R, I, A, S, E and C) and their hexagonal arrangement. A three-letter code then identifies the three types on which the person scored most highly. The congruence between a person and their environment (e.g. workplace or field of study) may affect their satisfaction and performance, and how to define congruence is a question of long standing. The method proposed here is based on (a) the presence and position of each of the six Holland types in the two three-letter codes being compared (or their absence from the codes) and (b) proximities of all pairs of types, reflecting the hexagonal arrangement of the types. There is discussion of whether the hexagonal arrangement ought to be used in calculating congruence, but a definite answer is not yet clear.

Letter to the editorTimothy P Hutchinso

Impact testing of pedestrian headforms is usually conducted at one velocity and with one mass of headform, but real impacts occur at a range of velocities and masses. A method is proposed to predict the Head Injury Criterion (HIC) and similar quantities at other velocities from their values observed under test conditions. A specific assumption is made about acceleration during the impact as related to displacement, its differential (instantaneous velocity), mass of headform, and initial velocity: namely, that it is the product of a power function of displacement (representing a possibly nonlinear spring) and a term that includes a type of damping. This equation is not solved, but some properties of the solution are obtained: HIC, maximum acceleration, and maximum displacement are found to be power functions of mass of headform and initial velocity. Expressions for the exponents are obtained in terms of the nonlinearity parameter of the spring. Simple formulae are obtained for the dependence of HIC, maximum acceleration, and maximum displacement on velocity and mass. These are relevant to many types of impact.