Determining the invariant power of a jet engine and resolving the "thrust paradox" within classical mechanics

Abstract (Description):This paper presents a rigorous derivation of the mechanical power and efficiency equations for a jet engine within the framework of classical mechanics. It is demonstrated that the well-known contradiction in jet propulsion theory, often referred to as the thrust power paradox or the energy anomaly of the Oberth effect, arises from a methodological error in which only the kinetic energy increment of the vehicle itself is considered, while the kinetic energy of the ejected working fluid is completely ignored. Based on the law of conservation of energy for a momentum-closed system comprising both the rocket and the exhaust jet, it is proven that when calculating total power, the terms containing the vehicle velocity strictly cancel out. Consequently, the power of a jet engine is an objective, invariant parameter that does not depend on the flight speed or the choice of an inertial reference frame. Physically, it equals the kinetic energy of the exhaust jet generated by the engine per unit time, which completely eliminates any apparent violation of the law of conservation of energy. Furthermore, the paper substantiates the necessity of distinguishing between the kinematic power distribution ratio and the true thermodynamic efficiency, which is defined as the ratio of the kinetic energy of the exhaust jet to the total chemical and thermal energy of the consumed fuel. this is the English translation of the main article