As described on the forces slide, the
is the sum of the lift of all of the
airplane and acts through the aircraft
center of pressure.
Each part of the aircraft has its own lift component and its own center
of pressure. The major part of
the lift comes from the wings, but the horizontal stabilizer and
elevator also produce lift which can be
varied to maneuver the aircraft.
The average location of the weight of the aircraft is the
center of gravity (cg).
Any force acting at some distance from the cg
torque about the cg.
Torque is defined to be the product of the
force times the distance.
A torque is a "twisting force" that
produces rotations of an object.
In flight, during maneuvers, an airplane rotates
about its cg.
But when the aircraft is not maneuvering, we want the rotation about
the cg to be zero.
When there is no rotation about the cg the aircraft is said to be
On most aircraft, the
center of gravity
of the airplane is located
near the center of pressure of the wing.
If the center of presure of the wing is aft of the center
of gravity, its lift produces a counter-clockwise rotation about
the cg. The center of pressure for the elevator is aft of the
center of gravity for the airliner shown in the figure.
A positive lift force from the tail
produces a counter-clockwise rotation about the cg.
To trim the aircraft it is necessary to
balance the torques produced by the wing and the tail.
But since both rotations
are counter-clockwise, it is impossible to balance the
two rotations to produce no rotation.
However, if the tail lift is negative it then produces a
clockwise rotation about the cg which can balance the wing rotation.
Let us look carefully at the torques produced by the wing and the tail.
The torque from
the wing TW is equal to the lift of the wing W times the distance
cg to the center of pressure of the wing dw.
TW = W * dw
The torque from the tail
TT is equal to the lift of the tail T times the distance from the
cg to the center of pressure of the tail dt.
The lift of the wing and the lift of the tail are both forces
and forces are
which have both a magnitude and a direction.
We must include a minus sign on the lift of the tail
because the direction of this force is negative.
TT = -T * dt
In trimmed flight, these
two torques are equal:
TW = TT
W * dw = -T * dt
W * dw + T * dt = 0
The torque equation, as written here, is a
All of the quantities
are vector quantities having a magnitude and a direction.
If the distances are both positive (same side of the center of gravity),
then the direction of the tail force must be different than the direction
of the wing force to produce no net torque or rotation.
However, if the distance to the tail were negative, then the lift of the
of the tail could be positive and there would be no net torque.
A negative distance to the tail would imply
that the tail is on the front of the aircraft, ahead of the center of gravity.
A tail at the front of the aircraft is called a canard and was
the configuration first used by the Wright brothers.
The total lift of the aircraft is the
of the wing lift and the tail lift. For the airliner, the total
lift is less than the wing lift; for the Wright brothers, the total
lift is greater than the wing lift.
The added lift was important for the Wright brothers because their
aircraft had a very small engine and flew at low speeds (35mph). Since
lift depends on the
square of the velocity, it is hard to generate
enough lift for flight at such low speeds.
Basic Aircraft Motion:
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