CLASSIFICATION

The motion impulse of the engine is equal to the air mass multiplied by the speed at which the engine emits this mass:
I = m c where m is the air mass per second and c is the exhaust speed. In other words, the plane will fly faster if the engine emits the air mass with a higher speed or if it emits more air per second with the same speed. However, when the plane flies with certain velocity v, the air moves towards it, creating the opposing ram drag at the air intake:
m vMost types of jet engine have an air intake, which provides the bulk of the gas exiting the exhaust. Conventional rocket motors, however, do not have an air intake, the oxidizer and fuel both being carried within the airframe. Therefore, rocket motors do not have ram drag; the gross thrust of the nozzle is the net thrust of the engine. Consequently, the thrust characteristics of a rocket motor are completely different from that of an air breathing jet engine.
The air breathing engine is only useful if the velocity of the gas from the engine, c, is greater than the airplane velocity, v. The net engine thrust is the same as if the gas were emitted with the velocity c-v. So the pushing moment is actually equal to
S = m (c-v) The turboprop has a wide rotating fan that takes and accelerates the large mass of air but only till the limited speed of any propeller driven airplane. When the plane speed exceeds this limit, propellers no longer provide any thrust (c-v < 0).
The turbojets and other similar engines accelerate much smaller mass of the air and burned fuel, but they emit it at the much higher speeds possible with a de Laval nozzle. This is why they are suitable for supersonic and higher speeds.
From the other side, the propulsive efficiency (essentially energy efficiency) is highest when the engine emits an exhaust jet at a speed that is the same as the airplane velocity. The exact formula, given in the literature,[3] is
The low bypass turbofans have the mixed exhaust of the two air flows, running at different speeds (c1 and c2). The pushing moment of such engine is
S = m1 (c1 - v) + m2 (c2 - v) where m1 and m2 are the air masses, being blown from the both exhausts. Such engines are effective at lower speeds, than the pure jets, but at higher speeds than the turboshafts and propellers in general. For instance, at the 10 km attitude, turboshafts are most effective at about 0.4 mach, low bypass turbofans become more effective at about 0.75 mach and true jets become more effective as mixed exaust engines when the speed approaches 1 mach - the speed of sound.
Rocket engines are best suited for high speeds and altitudes. At any given throttle, the thrust and efficiency of a rocket motor improves slightly with increasing altitude (because the back-pressure falls thus increasing net thrust at the nozzle exit plane), whereas with a turbojet (or turbofan) the falling density of the air entering the intake (and the hot gases leaving the nozzle) causes the net thrust to decrease with increasing altitude. Rocket engines are more efficient than even scramjets above roughly Mach 15