The propulsion system of an aircraft must
perform two important roles:
- During cruise, the engine must
provide enough thrust, to balance the
aircraft drag while using as little
fuel as possible.
- During takeoff and maneuvers, the
engine must provide additional thrust to accelerate the
aircraft.
Thrust T and drag D are forces and are
vector quantities
which have a magnitude and a direction associated with them.
The thrust minus the drag of the aircraft is called the excess
thrust and is also a vector quantity.
Considering Newton's second law
of motion, mass m times acceleration a is equal to
the net external force F on an object:
F = m * a
For an aircraft, the horizontal net external force Fh is the excess
thrust Fex.
Fex = Fh = T - D = m * a
Therefore, the acceleration of an aircraft is equal to the
excess thrust divided by the mass of the aircraft.
a = (T - D) / m
The thrust divided by the mass of the aircraft
is closely related to the thrust
to weight ratio. Airplanes with high excess thrust, like fighter
planes, can accelerate faster than aircraft with low excess
thrust.
If the excess thrust and the mass remain constant, the basic equation of
motion can be easily
solved
for the velocity and displacement as a function of time.
This equation can be used only if the force (and the
acceleration) are constant. Unfortunately for aircraft, drag is a
function of the square of the velocity. So we
can assume a constant force for only a very small amount of time. To
solve the actual equations of motion for an aircraft, we must use
calculus and integrate the equations of motion, either analytically
or numerically.
Activities:
Guided Tours
-
Forces on an Airplane:
-
Gradual Climb:
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