Standardized Description of the Generation Principle and Process of the Surface of Archimedes Spiral Wind Blade

Currently, there are three fundamental theoretical issues that need to be addressed in the research field of the Archimedes Spiral Wind Blade (ASWB): (1) the existing description of the generation principle of the ASWB’s surface is qualitative, which needs to be formally described using mathematical tools; (2) in the published literature, no studies were found that attempt to fully describe the surface of the ASWB using mathematical tools; (3) in the published literature, no clear definition of the ASWB can be found. The first and second of the above three problems are relatively easy to solve, whereas the ultimate solution to the third problem requires long-term communication and discussion among researchers from various countries. Therefore, this paper focuses primarily on the first of the above problems, namely, to describe the intermediate process of transforming an irregular planar figure into the 3D surface of an ASWB in a standardized manner using mathematical tools including a polar coordinate system, planar and spatial Cartesian coordinate systems, the curve equation of an Archimedes spiral, differential equations, and so on. For the second problem, this paper proposes an alternative approach: namely, conjecturing that the ASWB surface can be approximated by an infinite number of 3D Archimedes spirals, and an example with a finite number of such spirals is provided. For the third problem, this paper can currently only suggest that the precise definition of the ASWB should be based on a standardized description of the generation principle of the ASWB surface, or, alternatively, on an accurate geometric description of the shape of the ASWB surface. The scientific contribution of this paper lies in proposing, for the first time from a purely geometric perspective (independent of aerodynamics), three fundamental theoretical problems concerning ASWB, along with preliminary alternative ideas toward their solution.