If you want to save money and energy with your fans, motors, and turbo compres­sors, effi­ciency – or η – is prob­ably the most impor­tant indi­cator. After all, it shows how effi­ciently machines can convert power input into useful power output. If effi­ciency is high, a large propor­tion of power input gets to where it is supposed to go. If, on the other hand, it is low, power is mainly lost as waste heat.

The effi­ciency referred to in this attrac­tive formula is the overall effi­ciency η_overall of an oil-free turbo compressor. It is the math­e­mat­ical product of many other effi­cien­cies, namely of each indi­vidual compo­nent that delivers power when compressing refrig­er­ants and other gases.

This includes upstream power elec­tronics ­(η_{Power­Elec­tronics}), which control and transmit the elec­tric current to the motor, as well as the motor (η_Motor), which converts the elec­trical energy into mechan­ical energy. The effi­ciency of the oil-free gas bear­ings (­η_GasBearing) is also impor­tant. This is because it provides infor­ma­tion on how smoothly the rotor is running, in terms of power loss and wear, with the compressor impeller in the bearing, in order to rotate at up to 300,000 revo­lu­tions per minute and compress gases effi­ciently.

The last piece of the puzzle for calcu­lating the overall effi­ciency of a compressor is the effi­ciency of the compressor stage with the compressor impeller (­P_{Aero­dy­namics}). Compared with the other compo­nents, this formula breaks down exactly how this effi­ciency is made up. First, the ideal power consump­tion of the compressor stage (P_Aero,isen) – i.e. the power that the stage could provide if there were no losses.

Second, the actual power consump­tion (P_Aero) and the power loss due to leakage (P_Leakage). The ratio of the ideal power to the power actu­ally used, including leakage, is then used to describe the effi­ciency of the compressor stage. Finally, the effi­cien­cies of all the compo­nents can be multi­plied together. The result is the overall effi­ciency of the turbo compressor: a value between 0 and 1. A result of 0.7 means that the turbo compressor uses 70 percent of the power used to compress gases.