MODELING AND COMPUTER IMPLEMENTATION OF A SURFACE PORTION ON THE BASIS OF “CLOTHOID” CURVES

Abstract

When designing the contours of machines and units that work in a moving environment, ensuring a smooth change in curvature plays an important role. The law of curvature change is very important in this case, because the kink of the curvature along the surface inherits the turbulent stall of the flow of the moving medium, which increases the resistance of the unit to the moving medium. An increase in resistance to a moving environment leads to a decrease in the speed of movement. And when used in aircraft construction, the disruption of the moving environment can lead to a peak and crash of the aircraft. The integral curve of the "clothoid" is known. Its peculiarity lies in the fact that along the curve its curvature changes according to a linear law. Therefore, the use of this curve for constructing a surface can provide a linear law of change in curvature along the surface.

The paper considers the construction of a portion of the surface based on the curves of the "clothoid", which allows you to set the curvature at the boundaries of the portion and provide a linear law of its change over the portion surface. On the basis of such portions of the surface, it is possible to determine both surface stripes and three and quadrangular portions of the surface. In this case, the curvature changes linearly along the longitudinal directions and also along the transverse directions, because both along and across the portion there is a "clothoid" curve. And, as you know, the curvature along the clothoid changes linearly. It is advantageous to use the indicated strips and portions of surfaces in the design of surfaces of machines and assemblies, working in a moving environment (surfaces of aircraft, cars, ships), in which it is important to set a smooth law of curvature change along the surface. The law of curvature change is very important in this case, because the kink of the curvature along the surface inherits the turbulent stall of the flow of the moving environment, which increases the resistance of the unit to the moving environment. An increase in resistance to a moving medium leads to a decrease in the speed of movement. And when used in aircraft construction, the disruption of the moving environment can lead to a peak and crash of the aircraft. In works [1,2,3] various variants of surface portions are considered, but none of them provides a linear law of curvature change.

Key words: strip of surface, portion of surface, curvature, linear law of change of curvature, “clothoid” curve.