## 1 Introduction  
The first study on electrohydrodynamic propulsion was carried out in 1920 by [PERSON] and [PERSON], who hypothesized that the electric field interacted in some way with the gravitational field, in what they called the Biefeld-Brown Effect [1, 2]. Subsequent studies confirmed that the gravitational field was unaffected, and that the thrust was produced by a phenomenon now known as ionic wind. For the Biefeld-Brown effect and the ionic wind to occur, two electrostatic forces and a neutral fluid are required. When a high potential difference, of the order of kV, is applied between two electrodes, one acting as the anode or emitter and the other as the cathode or collector, the fluid surrounding the anode is ionized and the resulting ions are pushed towards the collector [3, 4], creating a net thrust in the opposing direction to the direction of ion flow, without moving parts or gas emissions. From these initial studies, research continued, firstly, the Biefeld Brown effect was analyzed in depth; in [5] the invalidity of [PERSON]'s assumption of a possible connection of gravitation with electromagnetism was demonstrated and some previous results obtained in near-vacuum conditions were also studied. NASA studied this phenomenon in 2004, [6], in a way closer to the study conducted in this article by proposing the use of asymmetrical capacitors (ACTs). In this research, they qualitatively predicted how the magnitude of the thrust changed as the design of the ACT varied. Tests were also performed in nitrogen and argon at reduced pressures. They concluded that Biefeld-Brown effect was fully explained by a very simple theory that uses only electrostatic forces and the transfer of momentum by multiple collisions. Since then, even more detailed studies have been carried out, such as the one presented in [7] which an experimental and theoretical analysis where the mobility of the ions and the dissipation of energy in the form of heat are evaluated. In 2013 a complete set of equations was obtained, [8], for an asymmetrical capacitor. The paper was aimed at the optimization of electrical and geometrical parameters of this type of thruster as well as to obtain a simple mathematical model. One of the first studies that tried to assess the feasibility of using ionic wind for electric propulsion flight was presented in 2014, [9]. The calculation of the thrust force for different configurations of thrusters was thoroughly analyzed. The methodology used presents common points with the one applied in this paper, but it did not introduce the energy study and W/g efficiency analysis. Even so, the global conclusion is coincident insofar as it proposed the use of several thrusters in cascade capable of producing considerable thrust values. In very similar terms, during the same year, another paper was published in which the aim was the optimization of the thrust produced by thrusters of very similar topologies manufactured in a \"handmade\" way, [10]. The number of publications in this field is large. Until 2019 the design of EHD thrusters is deeply analyzed, refined, and oriented towards space propulsion. During this period, one can find very deep and rigorous studies brilliantly developed more in the field of physics than that of engineering. In [11], a microfabricated atmospheric ion engine is presented. In 2017 three extensive publications can be found where different types of EHD thrusters are comprehensively analyzed. In [12] the results of the modeling of single stage EHD thrusters with different cathode configurations working at sub-atmospheric pressure are shown. In [13], a one-stage EHD thruster with a funnel-like cathode that uses nitrogen is thoroughly studied. Finally [13], in a comprehensive manner, summarizes [12] and [13]. Despite its high energy efficiency, this type of propulsion is limited by the difficulty of producing a very limited thrust, unless a thorough and complex study is made on how to redesign the thrusters and use the aircraft cell itself to install to increase it.