The choice of the main parameters of a turbofan and turbocompressor at the initial stage of two-spool turbofan engine design is considered. To optimize rotation speeds, the number of stages, and determine the diametrical dimensions, line H is highlighted on Smith charts for compressors, and line L –for turbines. These lines are constructed through the tangent points of constant efficiency isolines and parabolas of the formТН/2ac=const and UL/2ac=const. Expressions are proposed that make it possible to determine the values of the total pressure recovery ratio σ at each point of the Smith diagrams for compressorand turbine stages (at corresponding temperature values). Taking this into account, an original method for determining the efficiency of compressors and turbines is proposed. It is shown how to use Smith diagrams to determine parameters not only for complete stages, but alsofor elementary stages in different sections along the height of the flow path. The proposed method makes it possible to maximize the efficiency of turbines due to the appropriate choice of the number of stages, the distribution of total head rise and the position of the mass-average points “mid” for the stages on the Smith diagrams. It is shown how these methods are used when fine-tuning compressors and turbines based on the results of turbofan engine tests