Cylindrical capacitors are largely employed in avionic industry as contact submerged probes of level sensors for in-flight oil-level monitoring for many reasons: their high robustness, their long MTBF (Mean Time Between Failures), maintenance-free character, virtually infinite resolution readings and last, relatively low cost. However, the cylindrical capacitors suffer from low sensitivity mainly due to small oil permittivity. This is clearly a disadvantage which collides with the ever-increasing demand for higher static and dynamic performances. To improve that, the approach adopted here consists in tweaking the conventional design of this kind of sensors guided by the study of their limitations in terms of static errors and poor responsiveness caused by phenomena of capillarity, high viscosity, and vibrations. Indeed, sensitivity doubling is proved to be achieved without compromising the indispensable former qualities. This is shown by the results of electrostatic, fluid mechanics, and structural dynamics analyses presented with enough details. Numerical simulations have been carried out and are here presented to confirm results. To summarize, with respect to the conventional capacitive level sensors currently available on the market, the achievements of the proposed design are i) an improved sensitivity that, for engine oils, is greater than 700pF/m, ii) a lower cost even though extra-costs for surface perforation must be accounted for, iii) cancellation of systematic error due to capillary phenomena and iv) improved dynamic response. Also, accurate experimental verifications are being carried out and will be shared in a future paper.