There are four forces that act on an
aircraft in flight:
of the aircraft through the air depends on the relative size of the
various forces and the orientation of the aircraft. For an aircraft
in cruise, the four forces are balanced,
and the aircraft moves at a constant velocity and altitude.
Some modern fighter aircraft can change the angle of the thrust
by using a movable
The ability to change the angle of the thrust is called
thrust vectoring, or vectored thrust.
having a magnitude and a direction. The resulting
velocity and displacement of the aircraft are also vector
quantities which can be determined by
Newton's second law of
motion and the rules of
There are two
equations for the force on an aircraft.
One equation gives the
the net vertical force Fv, and the other gives the
net horizontal force Fh.
If we denote the thrust by the symbol T, the lift by L,
the drag by D, and the weight by W,
the usual force equations for an aircraft in level flight are:
Vertical: L - W = Fv
Horizontal: T - D = Fh
The quantity (T - D) is called the
and is related to the aircraft's ability to accelerate. Good fighter
aircraft have high excess thrust. The ability to
and maneuver involves the vertical net force as well as the excess thrust.
Since the thrust force is already a large force for fighter aircraft,
designers have sought ways to bring this force into the vertical
equations of motion. With new mechanical systems it is possible to
deflect the engine exhaust from the nozzle and cant the
thrust vector at an angle. We will call this angle c. The
resulting force equations are shown on the slide:
Vertical: L - W + T sin(c) = Fv
Horizontal: T cos(c) - D = Fh
where sin and cos are the
trigonometric sine and cosine functions.
The thrust now appears in the vertical force equation.
This allows the aircraft to climb faster than an aircraft without
thrust vectoring and to execute sharper turns than an un-vectored
For moderate angles, the cos is nearly equal to one, so the
aircraft still has high excess thrust.
The horizontal acceleration ah and vertical acceleration
av of the aircraft are given by:
av = Fv /m
ah = Fh /m
where m is the mass of the aircraft.
The only serious penalty for having vectored thrust is that
the nozzle is heavier than a standard nozzle.
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