Mathematical Modeling of the Route of Logging Roads

Abstract

The implementation of tasks related to the development of the transportation network as a whole and logging roads as an integral part of it requires scientifically based theoretical studies of the patterns of formation of spatial curves when combining elements of the plan and the longitudinal profile, since the rational laying of the route for many years determines its most important transport and operational characteristics (speed, traffic safety, traffic capacity). Consideration of the visual perception of the road by the driver will improve the quality of design decisions, which will allow to avoid emergencies in the future after setting the route into service. On the other hand, a decrease in speed before seemingly sharp turns of the road affects the efficiency of logging road transport. Therefore, the view of the road ahead should strongly orient the driver, i.e. be visually clear and clearly changing, ensuring the constancy or smooth reduction of the traffic flow mode. At the same time, the need for a successful spatial solution of the road increases. In the designs of logging roads, straight lines, transition curves, described in recent years most often according to the clotoid, and circular curves are found as elements of the route plan. It is found that the road view in perspective correctly orients the driver of the car, i.e. it is visually clear, provided that the lines describing the edges of the roadway and the edges of the roadway in the perspective image are curved in the same direction as in the road plan. The purpose of the work is to determine a set of quantitative indicators (curvature, radius of the curve in the plan, maximum curvature, maximum rate of change of curvature) for optimization of the visual smoothness and clarity of the central projections of elementary spatial and plane curves. The performed studies allow us to fully characterize the visual smoothness and clarity of the central projections of elementary spatial and plane curves. The above algorithm makes it possible to compile a computer program to determine the mentioned indicators. The indicators determined by this algorithm allow us to evaluate both the visual smoothness and clarity of curves on logging roads.