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A jet engine is an aircraft engine used to provide p ropulsion for a vehicle by ejecting a substance flow, i.e., creating a reactive force (thrust) which is applied against the vehicle. The jet (stream) can be continuous or discontinuous, gaseous or liquid, or in the form of ions, electrons, photons, etc. or separate solid particles. According to their design and the way the thrust is developed, jet engines are classified into two types: those using an outer medium (for instance air-jet engines or water-jet engines (ship engines)); and those which are independent of the outer medium, whose working substance is in the vehicle proper such as rocket engines (liquid-propellant), solid-propellant, ion-plasma jet, photon, etc.

Jet engines are characterized by the thrust R and the flow rate (kg/s) of the working substance; is the sum of the fuel flow f and the oxidant (air in air-jet engines) flow a. Such engines are also characterized by their overall dimensions (length, diameter, midsection); overhaul period; reliability (mean time between failures); and by ecological characteristics such as noise, exhaust gas composition, radiation, etc.

The thrust of a jet engine is generally expressed in terms of the exhaust velocity W of the working substance, the pressure pn at the nozzle cross-section at an area Fn and the flight velocity V in air with a pressure pH:


where for air-jet engines, β is the fuel mass-to-air flow ratio per second; for rocket engines, β = 0 and V = 0 because the fuel propels together with the vehicle. The jet engines can have a thrust of from 10−2 N in ion-plasma jet engines to 107 N in liquid-propellant rocket engines and 103−3 × 105 N in air-jet engines.

The efficiency of converting the kinetic energy of a jet into useful work of engine propulsion is estimated by the flight efficiency


The major parameters characterizing jet engines are

(a) Thermo- and gas dynamic performance:

Measures of performance include the specific impulse Jsp (thrust-to-working substance flow rate ratio, (R/ ) or the specific thrust Rsp (thrust-to-air flow rate ratio in air-jet engines, R/ a). Jsp is highest in photon engines (3 × 108). It is 104 × 105 in ion-plasma jet engines and 4 and 3 × 103 in liquid-propellant and solid-propellant rocket engines, respectively. In air-jet engines, Rsp varies from 102 to 1.5 × 103 Ns/kg.

Specific thrust is related to the useful work (Lc) of the thermodynamic cycle through which the engine generates jet kinetic energy


in this case, V = 0 for rocket engines.

Another important parameter is the specific consumption of the working substance CR (in air-jet engines, of fuel), i.e., flow rate-to-thrust ratio. The total efficiency of the engine is given by:


where Hu is the heat of combustion. η0 is equal to the product of the flight efficiency ηf and the efficiency of the cycle ηt

In rocket engines, CR = 1/Jsp, i.e., 10−2−10−9; and in air-jet engines, CR ≈ 0.3 × 10-2 kg/sN.

(b) The design effectiveness:

A design objective is to increase the ratio of mid-section thrust (Rf) to the mass of the engine.

Operating Process and Main Parameters of Air-Jet Engines

The conversion of heat energy released in fuel combustion in air-jet engines into the kinetic energy of a jet issuing from the engine and developing a gas thrust occurs in the cycle at constant pressure (Brayton's cycle). An air stream at a velocity V, pressure pH and temperature TH taken in by the engine is initially compressed due to retardation in the air intake (ΠV = pin/pH) and further compressed due to mechanical energy supply in the compressor (Πc = pc/pin). The air is heated by the fuel combustion in the combustion chamber to a temperature Tg and then is expanded first in the turbine (ΠT = pg/pT), which rotates the compressor and auxiliary units, and later in the nozzle (Πn = pT/PH), accelerating up to a preset exhaust velocity W.

Figure 1 shows the effect of the parameters Tg/TH and Πc on a turbojet engine in ground conditions (H = 0 km, Ma = 0, i.e., for TH = 228 K) and in flight conditions Ma = 2.2, H = 11 km relative to the Rsp-CR coordinates.

The maximum temperature of the gas in the Tg cycle (in gas-turbine engines, the temperature before the turbine) determines the efficiency of all types of air-jet engines (Rsp and CR) first. At a temperature Tglower than Tgmin, based on the equality of terms on the right-hand side in Eq. (1), air-jet engine efficiency cannot be realized at all. The degree of pressure increase has only a slight effect on air-jet engines.

The rise in values of Tg in gas-turbine air-jet engines from 800°C (in 1940) up to 1,500°C (by 1990) has been realized by enhancing the high-resistance alloys used and, to a greater extent, by the introduction and improvement of methods for cooling the first-stage turbine blades, the turbine (rotor) blade and the nozzle guide vane. Rotor blades work under especially severe conditions; military air-jet engines have circumferential speeds of 500-600 m/s at a gas temperature of up to 1,500°C. The requirements of long-term strength and low-cycle thermal fatigue dictate the following temperatures of blade walls from modern alloys: for rotor blades, not higher than 850-950°C and for nozzle guide vanes, up to 1000-1100°C. Air bled from the compressor is passed through the blades to cool them from within.

Fuel flow to thrust ratio (CR) as a function of the thrust to air flow rate ratio (Rsp).

Figure 1. Fuel flow to thrust ratio (CR) as a function of the thrust to air flow rate ratio (Rsp).

Cooling efficiency depends on the complexity of the internal structure of the blade and on the ratio of air flow rates—cooling air vs. that flowing around the outside of the blade, δ = c/a. Figure 2 characterizes the efficiency of cooling θ = (Tg - Tbl)/(Tg - Tc) of a series of blade cooling schemes. Thus, the value θ = 0.5, which corresponds to equal temperature drops between gas flow and the blade and between the blade and cooling air, is characteristic of a high degree of heat exchange intensification inside the blade (intricate eddy flows and a specially developed heat transfer surface) because the gas velocity on the outside of the blade is 10 times higher than the air velocities inside it. The values of δ are usually in the range 2.5-5%. To increase Tg, intermediate air bled from the compressor is often cooled in a special heat exchanger with fuel cooling capability.

The entry of cooling air into the flowing duct, as a rule, diminishes the flow around the turbine blades, reducing their efficiency. But in this case, the useful effect of a gas temperature rise reduces the deterioration in efficiency.

The most efficient turbines are the high-temperature turbines made from super heat-resistant materials (ceramics, composites, etc.). This is the main trend in the development of future air-jet engines in which only blades made from silicon carbide and niobium are used, which operate at gas temperatures of about 1,300°C. The technological difficulties associated with the manufacture of a less than 1 mm thick ceramic blade training edge, however, make their efficiency worse than that of metal blades and, therefore, prevents the complete elimination of cooling mechanisms.

Cooling efficiency for various types of blade cooling in jet engines.

Figure 2. Cooling efficiency for various types of blade cooling in jet engines.

Effect of bypass ratio in overflow rate-to-thrust ratio.

Figure 3. Effect of bypass ratio in overflow rate-to-thrust ratio.

In air-jet engines of more intricate designs, by-pass engines (with or without mixing of flows from a turbofan, or an outer duct, or a turbocompressor, or an inner duct) with thrust augmentors are employed and the parameters Rsp and CR are usually used. Turbojet by-pass engines are now the main type of aircraft engines used in both civil and military aviation. Figure 3 shows how higher flight efficiencies (Eq. (2)) are obtained at the expense of larger air masses with lower exhaust velocities (a large value of the by-pass ratio m = GaII/GaI = 3-6) and, accordingly, of smaller CR when H = 11 km, M = 0.8 and Tg = 1600 K. In order to obtain minimum CR for the given flight conditions and with a turbocompressor selected (Tg and Π), the optimal combinations of by-pass ratio m and relative pressure increase in the fan ΠF—governed mainly by the requirement for equal conditions of flow pressures issuing from both ducts—can be determined. An increase in the by-pass ratio is always accompanied by the need to reduce the ΠF, causing a decrease in specific thrust and a rise in the overall dimensions of an engine. It is the size of the latter in aircraft conditions (in the wing geometry and taking account of the total outer aerodynamic drag) that restricts the tendency for a decrease in m, starting with the reduction of C R.

Figure 4 shows the effects of the various degrees of upgrading (with respect to specific thrust and fuel consumption) turbojet engines can undergo by feeding additional (afterburn) fuel into the air duct behind the turbine, i.e., the effect of gas temperature in the thrust augmentor of a turbojet engine, with Π c = 8, Tg == 1,400 K.

Effect of afterburn on engine performance.

Figure 4. Effect of afterburn on engine performance.

Operating Characteristics of Air-Jet Engines

The conditions in which air-jet engines are operated determine the changes in their main parameters (the thrust and the fuel consumption) with velocity (Mach number), flight altitude (H) of the aircraft and the operation mode of the engine. Engine parameters change considerably at ground conditions with the temperature of the surrounding air.

The typical operating modes of air-jet engine operation are: maximum mode (with maximum permissible gas temperature and r.p.m.) where the time is usually limited and applications are during takeoff and acceleration of the aircraft; the maximum continuous power mode (80-85% thrust and 95% r.p.m.), with unlimited time and used, for instance, in climbing; cruising power mode (80-85% thrust and this is usually the condition of highest efficiency), the most continuous and idling power mode (5-7% thrust), a holding mode. In some cases (as a rule, in turboshaft engines) a contingency power mode exists.

Air-jet engines with a thrust augmentor (afterburn systems) have additional modes: maximum reheat power, i.e., with a maximum thrust for limiting n, Tg and TF (at take-off or at target interception); the mode of partial thrust augmentation, with a decreased n, TF and even Tg and unlimited time of operation used, for instance, in continuous supersonic flight and the minimal afterburning mode, defined by sustained combustion in the thrust augmentor and required for greater smoothness of control.

The change in the thrust with height, velocity of flight and mode is connected to the level of maximum gas temperature in the cycle, the temperature and pressure of the air which enters the engine, the values of pressure increase and with the efficiency of the elements under these conditions. These values, which enter into Eqs. (4) and (5), and the absolute values of air flow rate through the engine determine the thrust and the efficiency for the given M, flight altitude and rotor r.p.m. (n).

Air-jet engines operate under broad changes in environmental conditions, not only of the temperature and pressure of the feeding air but also of the degree of uniformity of the parameter fields W, P, T and their nonstationary characteristics. Such elements as air intake, the compressor and the combustion chamber have regions where their characteristics can be unstable (air flow separation, stall) and where either the operation can cease or damage due to the action of pulsations can occur. Agreement between the amount of fuel supplied under set conditions and the required charges in the geometry of the flowing duct (usually the guide vanes of the compressor and areas of the nozzle and air intake) is ensured by a system of computer based control which can take account of up to 12-14 optimal parameters.

Ram-jet engines are aircraft engines for high-speed flight in which the Brayton cycle is, as a rule, realized in flight conditions without a turbocompressor in the air intake-combustion chamber-nozzle system. Depending on the set flight velocity and on the characteristics of the main elements, ram-jet engines are classed as subsonic, super and hypersonic by the type of air intake; as having subsonic or supersonic velocities in the combustion chamber and as having continuous and pulsating action. Ram-jet engines are distinguished by a rapid increase in thrust with flight velocity due to a rise in pressure and in air density. But at flight velocities where the stagnation temperature of the air passing through the air intake into the combustion chamber approaches the combustion temperature (2,000-2,200 K), the warm-up decreases and the thrust diminishes drastically. Operation under conditions of supersonic combustion (such engines are called hypersonic ram-jet engines) considerably enlarges the application of ram-jet engines depending on flight Mach number. The real Ma for hypersonic ram-jet engines increases from 3-5 to 10-12.


Bathie, W. W. (1984) Fundamentals of Gas Turbines. John Wley and Sons.

Cohen, H., Rogers, G. F. S., and Saravanamutoo, N. J. N. (1987) Gas Turbines. Longman Scientific and Technical.

Ferry, A. (1969) Supersonic Turbojet Propulsion Systems and Components.

Wilson, D. T. (1984) Design of High-efficiency Turbomachinery and Gas Turbines. MIT Press.


  1. Bathie, W. W. (1984) Fundamentals of Gas Turbines. John Wley and Sons.
  3. Ferry, A. (1969) Supersonic Turbojet Propulsion Systems and Components.
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