This paper justifies recent trends in the mathematical definition of blade surfaces of impellers and rotors. The authors introduce a simple and efficient surface definition method, which is highly suited for numerical manufacture. Examples of a centrifugal compressor impeller, a mixed flow pump impeller and a gas turbine blade manufactured using the method are also presented.

In this first part the theoretical approach and the mathematical derivations of the authors STRAIGHT-LINE-SURFACE structure method is introduced.

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