Most aircraft designers prefer electric engines with open helices rather than ducted fan units. Open propellers often present a higher propulsive efficiency if compared to electric turbofans. High altitudes and rarefied atmosphere evidence this difference. A mathematical model to improve the performances of a ducted fan unit has presented. It aims to align the performances of the two systems by acting on the air intake of the ducted fan. It defines a simplified method for increasing the efficiency of an electric turbofan. It aims to produce a basic and solid mathematical model, which can apply to the study of this propulsion system. CFD simulations have verified the results. Two CFD codes have used to validate the results. An analysis of mesh independence has performed to ensure a better quality of the results. The presented model aims to reach also a methodological result. It tries to be an example of a plain engineering notation, drawn by basic physics and refusing a disciplinary and speciality symbols.