MODELING AND COMPUTER IMPLEMENTATION OF A SPLINE FROM CLOTHOID SEGMENTS

Abstract

When designing the contours of machines and units that operate in a moving environment, an important role is played by ensuring a smooth change in curvature.

The law of curvature change is very important in this case, because the curvature break 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 medium leads to a decrease in the speed of movement. And when used in aircraft construction, the disruption of a moving medium can lead to a peak and an aircraft crash.

The integral curve of the “clothoid” is known. Its peculiarity lies in the fact that along the curve its curvature changes according to the linear law. Therefore, the use of this curve to construct a surface can provide a linear law of change in curvature along the surface. The paper considers the construction of a spline consisting of clothoid segments, which provides a linear closed curvature change along the entire spline curve.

The specified spline is advantageous to use 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 specify the law of curvature variation along the surface.

The law of curvature change is very important in this case, because the curvature break along the surface inherits the turbulent stall of the flow of the moving medium, hich increases the resistance of the unit to the moving medium. 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 a moving medium can lead to a peak and an aircraft crash. The papers [1,2,3] consider various variants of surface portions, but none of them provides a linear law of curvature variation.

Key words: curvature, spline of clothoid segments, “clothoid” curve.