response to momentary disturbance is associated with its inherent degree of stability built in by the designer, in each of the three
axes, and occurring without any reaction from the pilot.
There is another
condition affecting flight, which is the aircraft's state of trim
or equilibrium (where the net sum of all forces equals zero).
Some aircraft can be trimmed by the pilot to fly 'hands off' for straight and level
flight, for climb or for descent.
Free flight models generally have to rely on the
state of trim built in by the designer and adjusted by the
rigger, while the remote controlled models have some form of trim
devices which are adjustable during the flight.
aircraft's stability is expressed in relation to each axis :
lateral stability (stability in roll)
directional stability (stability in yaw)
- longitudinal stability
(stability in pitch)
Lateral and directional stability are inter-dependent.
Stability may be defined as follows :
Positive stability - tends to return to original condition after a
Negative stability - tends to increase the
Neutral stability - remains at the new condition.
Static stability - refers to the aircraft's
to a disturbance.
Dynamic stability - refers to the aircraft
response over time to a disturbance.
So, a static
stable aircraft may be dynamically unstable.
Dynamic instability may be prevented by an even distribution of
weight inside the fuselage, avoiding too much weight
concentration at the extremities or at the CG. Also control
surfaces' max throws may affect the flight stability, since a too
much control throw leads often to dynamic instability.
totally stable aircraft will return, more or less immediately, to
its trimmed state without pilot intervention.
However, such an aircraft is rare and not much desirable. We
usually want an aircraft just to be reasonably stable so it is
easy to fly.
If it is too stable, it tends to be sluggish in maneuvering,
exhibiting too slow response on the controls.
instability is also an undesirable characteristic, except where an extremely maneuverable aircraft is needed and the instability can be
continually corrected by on-board 'fly-by-wire' computers rather
than the pilot, such as a supersonic air superiority fighter.
Lateral stability is achieved through dihedral,
sweepback, keel effect and proper distribution of weight.
The dihedral angle is the angle that each wing makes with the
horizontal (see Wing Geometry). If a disturbance causes one
wing to drop, the lower wing will receive more lift and the aircraft will roll back into the
A sweptback wing is one in which the
leading edge slopes backward. When a disturbance causes an aircraft with sweepback to slip or drop a
wing, the low wing presents its leading edge at an angle more perpendicular to the relative airflow. As a
result, the low wing acquires more lift and rises, restoring the
aircraft to its original flight attitude.
The keel effect occurs with high
wing aircraft. These are laterally stable simply because the
wings are attached in a high position on the fuselage, making the fuselage behave like a keel. When the aircraft is disturbed
and one wing dips, the fuselage weight acts like a pendulum returning the
aircraft to the horizontal level.
The tail fin determines the directional
stability. If a gust of wind strikes the aircraft from the right it will be in a slip and the fin will get an
angle of attack causing the aircraft to yaw until the slip is eliminated.
Longitudinal stability depends on the location of the
centre of gravity, the stabilizer area and how far the stabilizer
is placed from the main wing. Most aircraft would be completely
unstable without the horizontal stabilizer.
cambered airfoils have a higher lift coefficient, but they also have a negative pitching moment (Cm) tending to pitch nose-down, and
thus being statically unstable, which requires the counter
moment produced by the horizontal stabilizer to get adequate
longitudinal stability. The stabilizer provides the same function
in longitudinal stability as the fin does in directional
Symmetrical (zero camber) airfoils have normally
a zero pitching moment, resulting in neutral stability, which means the aircraft goes wherever you point it. Reflexed airfoils
(with trailing edge bent up) have a positive pitching moment making them naturally stable, they are often used with flying wings
(without the horizontal stabilizer).
It is of crucial
importance that the aircraft's Centre of Gravity (CG) is
located at the right point, so that a stable and controllable
flight can be achieved. In order to achieve a good longitudinal
stability, the CG should be ahead of the Neutral Point (NP),
which is the Aerodynamic Centre of the whole aircraft. NP is the
position through which all the net lift increments act for a change
in angle of attack. The major contributors are the main wing,
stabilizer surfaces and fuselage.
The bigger the stabilizer
area in relationship to the wing area and the longer the tail
moment arm relative to the wing chord, the farther aft the NP will
be and the farther aft the CG may be, provided it's kept ahead
of the NP for stability.
The angle of the fuselage to the direction of flight affects its
drag, but has little effect on the pitch trim unless both the projected area of the fuselage and its angle to the direction of
flight are quite large.
A tail-heavy aircraft will be
more unstable and susceptible to stall at low speed e. g. during
the landing approach.
nose-heavy aircraft will be more difficult to takeoff
from the ground and to gain altitude and will tend to drop its nose when the throttle is reduced. It also requires higher speed
in order to land safely.
The angle between the wing chord
line and the stabilizer chord line is called the Longitudinal
Dihedral (LD) or decalage.
For a given centre of gravity, there is a LD angle that results
in a certain trimmed flight speed and pitch attitude.
If the LD angle is increased the plane will take on a more nose up pitch attitude, whereas with a decreased
LD angle the plane will take on a more nose down pitch attitude.
There is also the
Angle of Incidence, which is the angle of a
flying surface related to a common reference line drawn by the
designer along the fuselage. The designer might want this
reference line to be level when the plane is flying at level
flight or when the fuselage is in it's lowest drag position.
The purpose of the reference line is to make it easier to set up the
relationships among the thrust, the wing and the stabilizer
incidence angles. Thus, the Longitudinal Dihedral and the Angle of Incidence are interdependent.
Longitudinal stability is also improved if the stabilizer is
situated so that it lies outside the influence of the main wing downwash. Stabilizers are therefore often staggered and mounted at a different height in order to improve
their stabilizing effectiveness.
It has been found both experimentally and
theoretically that, if the aerodynamic force is applied at a
location 1/4 from the leading edge of a rectangular wing at
subsonic speed, the magnitude of the aerodynamic moment remains
nearly constant even when the angle of attack changes.
This location is called the wing's
Aerodynamic Centre AC. (At supersonic speed, the aerodynamic centre is near 1/2 of the
In order to obtain a good Longitudinal Stability the Centre
of Gravity CG should be close to the main wings' Aerodynamic Centre AC.
For wings with other than rectangular form (such as triangular,
trapezoidal, compound, etc.) we have to find the Mean
Aerodynamic Chord MAC, which is the average for the whole
wing. See the drawings below:
For a delta wing the
CG should be located 10% ahead of the
geometrically calculated AC point as shown above.
The MAC of an elliptical wing is 85% of the root chord and is
located at 53% of the half wingspan from the root chord.
AC location for biplanes with positive stagger (top wing
ahead of the bottom wing), is found according to the drawing
For conventional designs (with main wing and horizontal stab)
the CG location range is usually between 28% and 33% from
the leading edge of the main wing's MAC, which means between
about 5% and 15% ahead of the aircraft's Neutral Point NP.
This is called the
Static Margin, which is expressed as a
percentage of MAC. When the static margin is zero (CG coincident
with NP) the aircraft is considered "neutrally stable".
However, for conventional designs the static margin should be
between 5% and 15% of the MAC ahead of the NP.
location as described above is pretty close to the wing's
Aerodynamic Center AC because the lift due to the horizontal stab
has only a slightly effect on the conventional R/C models.
However, those figures may vary with other designs, as the NP
location depends on the size of the main wing vs. the stab size
and the distance between the main wing's AC and the stab's AC.
The simplest way of locating the aircraft's NP is by using the areas
of the two horizontal lifting surfaces (main wing and stab) and
locate the NP proportionately along the distance between the main
wing's AC point and the stab's AC point. For example, the NP
distance to the main wing's AC point would be :
D = L ·
(stab area) / (main wing area + stab area) as shown on the picture
There are other factors, however, that make the simple
formula above inaccurate. In case the two wings have
aspect ratios (different dCL/d-alpha) the NP will be closer to
the one that has higher aspect ratio. Also, since the stab
operates in disturbed air, the NP will be more forward than the
simple formula predicts.
The figure below shows a somewhat
more complex formula to locate the NP but would give a more
using the so called Tail Volume Ratio, Vbar. This formula gives the NP position as a percentage (%) of the wing's
MAC aft of the wing's AC point.