How accurate should sight distance measurements be?

Abstract

Abstract We consider a situation, when braking is the only way to avoid obstruction of an automotive vehicle or a railroad train with a suddenly detected steadfast obstacle blocking the path. The velocity at the moment of the impact is viewed as a natural and a suitable criterion of the severity of the impact and, hence, of the very likelihood of the accident. Assuming that this velocity is distributed in accordance with the Rayleigh law, it is shown that the corresponding available sight distance (ASD) treated as a non-random function of the random impact velocity follows the exponential distribution. The variability (uncertainty) of the ASD measurements by the navigation system’s Radar(s) and/or Lidar(s) is assessed assuming that these measurements are normally distributed random variables. It is determined that the accuracy of these measurements, when the actual ASD is short and because of that the expected level of the impact velocity and, hence, the probability of the obstruction, are significant, is as important as the actual, objective, measurement independent ASD. The obtained information can be useful when choosing, developing and employing Radars and/or Lidars as effective navigation devices in various vehicular human-system-integration/interaction (HSI) technologies. This is true not only for the particular automotive or railroad situations in question, but also in other areas of vehicular engineering, such as, say, aerospace (e.g., when landing on Mars or on the Moon) or in maritime engineering (e.g., when encountering an obstacle, like another vessel or an iceberg, or when establishing an adequate under-keel clearance for large tankers navigated in shallow waters).