MATHEMATICAL MODEL OF THE MEASURING TRAJECTORY OF THE SOIL SURFACE AREAS BY CIRCULAR SCANNING WITH A LASER PROFILOGRAPH

Abstract

Background. The scientific article offers a mathematical model of the measuring trajectory of the soil surface areas, performed by a laser Profiler using the circular scanning method. Among the known contact methods for measuring surface irregularities, the pin method or profilometry is the most common, while ground-based laser scanning and digital photogrammetry are popular among non-contact methods. The subject of the study is the process of measuring different areas of the soil surface. The purpose of this work is to establish a mathematical model of the trajectory of measuring areas of the soil surface. Materials and methods. To measure the roughness of the soil surface profile, it is proposed to use a laser Profiler for circular scanning. The advantage of the Profiler is the high accuracy of measurement (±0.1 mm), which is provided by the laser sensor. Also, compared to devices that measure in a single longitudinal-vertical plane, the circular scan Profiler has dimensions up to 4–5 times smaller for a single scan length. Considering the process of measuring data during circular scanning in a Cartesian and polar system with the beginning of the system in the center of rotation of the sensor, systems of equations are established. Results. To obtain a mathematical model of the trajectory of measurement by a Profiler that scans along a circle of constant radius, the control of flat horizontal and inclined sections of the surface is theoretically studied. Graphically, the dependencies represent harmonic oscillations, where the value of the amplitude is determined by the value of the slope of the surface. The distance along the abscissa axis between the largest and smallest points of the ordinate is constant and equal to 180 degrees, and the slope direction is set based on them, taking into account the initial phase of the oscillation, which determines the value of the full phase of the oscillation at the moment φ = 0. Conclusions. For a circular scan with a laser profilograph flat horizontal and inclined sections set of circular and ellipsoidal trajectories of the measurement, respectively. Mathematical and graphical descriptions of data in Cartesian and polar coordinate systems are given, which allow determining the micro-relief of the soil surface, as well as the direction and slope of the slope. In further studies, it is proposed to evaluate the measurement trajectories obtained by laser circular scanning of convex and concave surface areas.

Keywords

• mathematical model
• measuring trajectory
• soil surface
• laser рrofiler
• circular scan