Jet Engine
Prof. Dr. Mustafa Cavcar
Anadolu University, School of Civil Aviation
Eskisehir, Turkey
GROSS THRUST
INTAKE
MOMENTUM
DRAG
NET THRUST
Figure 1 Jet engine
The thrust for a turbojet engine can be derived from Newton’s second law which
implies that the force equals to the time rate of change of momentum:
F=
d (mV )
dt
where mV is the momentum.
The net thrust of a jet engine is the difference between the outgoing exhaust gas
momentum flow and incoming air momentum flow. Outgoing exhaust gas
momentum is usually referred the gross thrust, and incoming air momentum flow
is called momentum drag or ram drag. Since m& = dm / dt is the mass flow rate of
the air passing through the engine, then the gross thrust
Tg = m& V j + A j ( p j − p am )
where
V j = exhaust gas velocity,
A j = area of jet nozzle,
p j = static pressure at the jet nozzle discharge, and
p am = atmospheric pressure.
The incoming air momentum flow (momentum drag)
Ti = m& Vi
© Prof. Dr. Mustafa Cavcar, 2004.
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where Vi is the incoming air velocity. Therefore, the net thrust
Net thrust = Gross thrust - Momentum drag
[
]
T = m& V j + A j ( p j − p am ) − m& Vi
= m& (V j − Vi ) + A j ( p j − p am )
Factors Affecting Jet Thrust
Air Velocity
Incoming air velocity affects
the thrust in two different and
opposite ways. When the
aircraft is static, as when an
engine is being run up prior to
take-off at the end of a
runway, momentum drag is
equal to zero, because Vi = 0 .
However, as the aircraft
commences to move, the
velocity of the air entering the
engine also begins to increase
because of the speed of the
aircraft.
Therefore,
the
difference between V j and Vi
Figure 2 Jet engine thrust versus airspeed [1].
will become less as airspeed,
or Vi , increases. On the other hand, as the aircraft gains speed down a runway, the
movement of the aircraft relative to the outside air causes air to be rammed into
the engine inlet duct. This compression of air in an inlet duct arising from forward
motion is called ram pressure or ram effect. The ram effect both increases the air
mass flow to the engine and the intake pressure, and consequently, increases the
thrust. Figure 2 shows how the thrust varies with airspeed considering both
velocity difference variation and ram effects.
However, ram pressure rise is not significant at lower speeds, thus it cannot offset
the effect of (V j − Vi ) difference and the thrust decreases as the aircraft speeds up
during take-off. Thrust decrease due to airspeed increase during take-off is more
significant for the turbofan engines as shown in Figure 3. Because the pure jet and
© Prof. Dr. Mustafa Cavcar, 2004.
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the lower by-pass ratio engines have less airflow per unit of thrust, they suffer less
momentum drag as speed increases.
Figure 3 Take-off thrust variation for various engines [2].
Air Temperature
The thrust generated by a jet
engine
is
inversely
proportional with the ambient
air temperature, thus the
thrust decreases as the air
temperature
increases.
However, this also means an
increase of thrust when the
temperature decreases, so that
an engine may generate
higher thrust than its design
rating at lower ambient air
temperatures. Higher thrust
above the design rating can
harm the engine. For this
reason, engines are restricted Figure 4 Thrust versus air temperature for a flat
to a maximum thrust. This rated engine.
thrust restriction is called
“flat rating,” and engines with restricted maximum take-off thrust are called “flat
rated.” At a given pressure altitude, temperature has no influence on engine
takeoff thrust, below the so-called reference temperature ( Tref ) or flat rating
© Prof. Dr. Mustafa Cavcar, 2004.
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temperature. Above this reference temperature, engine thrust is limited by the
Exhaust Gas Temperature (EGT). The consequence is that the available thrust
decreases as the temperature increases [3]. Thrust versus temperature for a flat
rated engine is shown in Figure 4.
Altitude
The effect of altitude on thrust is a
function of density. As the
altitude increases, the pressure
and density decreases so does the
thrust, but as the temperature
decreases, the thrust increases.
However, the pressure and density
of the outside air decreases faster
than the temperature, so an engine
actually produces less thrust as the
altitude is increased [1]. Because Figure 5 Thrust versus altitude.
temperature stays constant in the
stratosphere while pressure and density are decreasing as the altitude increases,
thrust will drop off more rapidly in the stratosphere as shown in Figure 5.
Combined Effects of Velocity and Altitude
Figure 6 Thrust versus Mach number for P&WC JT15D-4C Turbofan engine [4].
Figure 6 shows the maximum cruise thrust variation of JT15D-4C turbofan engine
with the Mach number for various altitudes. Since true airspeed is proportional
© Prof. Dr. Mustafa Cavcar, 2004.
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with the Mach number at a given pressure altitude, then these variations will be
similar for thrust versus airspeed case. As shown in the figure, thrust decrease to
the velocity increase is more significant at lower altitudes. As the altitude
increases, the thrust variation due to airspeed flattens, and even a slight increase
occurs at higher airspeeds.
References
[1]
United Technologies Pratt & Whitney, The Aircraft Gas Turbine Engine
and Its Operation, P&W Oper. Instr. 200, 1988.
[2]
R.S. Shevell, Fundamentals of Flight, Prentice Hall, Englewood Cliffs,
1989.
[3]
Airbus Industrie, Getting to Grips with Aircraft Performance, Blagnac,
2002.
[4]
United Technologies Pratt & Whitney Canada, JT15D-4C Fact Sheet,
Longueuil, 1987.
© Prof. Dr. Mustafa Cavcar, 2004.
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