In
flight dynamics
Flight dynamics in aviation and spacecraft, is the study of the performance, stability, and control of vehicles flying through the air or in outer space. It is concerned with how forces acting on the vehicle determine its velocity and attitude w ...
, longitudinal stability is the
stability
Stability may refer to:
Mathematics
*Stability theory, the study of the stability of solutions to differential equations and dynamical systems
**Asymptotic stability
**Linear stability
**Lyapunov stability
**Orbital stability
**Structural stabilit ...
of an aircraft in the longitudinal, or
pitching, plane. This characteristic is important in determining whether an
aircraft pilot
An aircraft pilot or aviator is a person who controls the flight of an aircraft by operating its directional flight controls. Some other aircrew members, such as navigators or flight engineers, are also considered aviators, because they a ...
will be able to control the aircraft in the pitching plane without requiring excessive attention or excessive strength.
The longitudinal stability of an aircraft, also called pitch stability,
refers to the aircraft's stability in its plane of symmetry
about the lateral axis (the axis along the
wingspan
The wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip. For example, the Boeing 777–200 has a wingspan of , and a wandering albatross (''Diomedea exulans'') caught in 1965 had a wingspan of ...
).
[ It is an important aspect of the handling qualities of the aircraft, and one of the main factors determining the ease with which the pilot is able to maintain level flight.]
Longitudinal static stability refers to the aircraft's initial tendency on pitching. Dynamic stability refers to whether oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
s tend to increase, decrease or stay constant.
Static stability
If an aircraft is longitudinally statically stable, a small increase in angle of attack
In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is m ...
will create a nose-down pitching moment
In aerodynamics, the pitching moment on an airfoil is the moment (or torque) produced by the aerodynamic force on the airfoil if that aerodynamic force is considered to be applied, not at the center of pressure, but at the aerodynamic center o ...
on the aircraft, so that the angle of attack decreases. Similarly, a small decrease in angle of attack will create a nose-up pitching moment so that the angle of attack increases.[ This means the aircraft will self-correct longitudinal (pitch) disturbances without pilot input.
If an aircraft is longitudinally statically unstable, a small increase in angle of attack will create a nose-up pitching moment on the aircraft, promoting a further increase in the angle of attack.
If the aircraft has zero longitudinal static stability it is said to be statically neutral, and the position of its ]center of gravity
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weight function, weighted relative position (vector), position of the distributed mass sums to zero. Thi ...
is called the ''neutral point''.
The longitudinal static stability of an aircraft depends on the location of its center of gravity relative to the neutral point. As the center of gravity moves increasingly forward, the pitching moment arm is increased, increasing stability. The distance between the center of gravity and the neutral point is defined as "static margin". It is usually given as a percentage of the Mean Aerodynamic Chord
In aeronautics, the chord is an imaginary straight line joining the leading edge and trailing edge of an aerofoil. The chord length is the distance between the trailing edge and the point where the chord intersects the leading edge.L. J. Clan ...
. If the center of gravity is forward of the neutral point, the static margin is positive. If the center of gravity is aft of the neutral point, the static margin is negative. The greater the static margin, the more stable the aircraft will be.
Most conventional aircraft have positive longitudinal stability, providing the aircraft's center of gravity lies within the approved range. The operating handbook for every airplane specifies a range over which the center of gravity is permitted to move. If the center of gravity is too far aft, the aircraft will be unstable. If it is too far forward, the aircraft will be excessively stable, which makes the aircraft "stiff" in pitch and hard for the pilot to bring the nose-up for landing. Required control forces will be greater.
Some aircraft have low stability to reduce trim drag. This has the benefit of reducing fuel consumption. Some aerobatic and fighter aircraft
Fighter aircraft are fixed-wing military aircraft designed primarily for air-to-air combat. In military conflict, the role of fighter aircraft is to establish air superiority of the battlespace. Domination of the airspace above a battlefield ...
may have low or even negative stability to provide high manoeuvrability. Low or negative stability is called relaxed stability
In aviation, relaxed stability refers to an aircraft with low or negative stability.
An aircraft with negative stability will have a tendency to change its pitch and bank angles spontaneously. An aircraft with negative stability cannot be trimm ...
. An aircraft with low or negative static stability will typically have fly-by-wire
Fly-by-wire (FBW) is a system that replaces the conventional manual flight controls of an aircraft with an electronic interface. The movements of flight controls are converted to electronic signals transmitted by wires, and flight control co ...
controls with computer augmentation to assist the pilot. Otherwise, an aircraft with negative longitudinal stability will be more difficult to fly. It will be necessary for the pilot devote more effort, make more frequent inputs to the elevator control, and make larger inputs, in an attempt to maintain the desired pitch attitude.[
For an aircraft to possess positive static stability, it is not necessary for its level to return to exactly what it was before the upset. It is sufficient that the speed and orientation do not continue to diverge but undergo at least a small change back towards the original speed and orientation.]
The deployment of flaps will increase longitudinal stability.
Unlike motion about the other two axes and in the other degrees of freedom of the aircraft (sideslip translation, rotation in roll, rotation in yaw), which are usually heavily coupled, motion in the longitudinal plane does not typically cause a roll or yaw.
A larger horizontal stabilizer, and a greater moment arm of the horizontal stabilizer about the neutral point, will increase longitudinal stability.
Tailless aircraft
For a tailless aircraft
In aeronautics, a tailless aircraft is an aircraft with no other horizontal aerodynamic surface besides its main wing. It may still have a fuselage, vertical tail fin (vertical stabilizer), and/or vertical rudder.
Theoretical advantages of the ...
, the neutral point coincides with the aerodynamic center
In aerodynamics, the torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift and net drag applied at some point on the airfoil, and a separate net pitching moment about that point whose magnitude ...
, and so for such aircraft to have longitudinal static stability, the center of gravity must lie ahead of the aerodynamic center.
For missiles with symmetric airfoils, the neutral point and the center of pressure are coincident and the term neutral point is not used.
An unguided rocket must have a large positive static margin so the rocket shows minimum tendency to diverge from the direction of flight given to it at launch. In contrast, guided missiles usually have a negative static margin for increased maneuverability.
Dynamic stability
Longitudinal dynamic stability of a statically stable aircraft refers to whether the aircraft will continue to oscillate after a disturbance, or whether the oscillations are damped. A dynamically stable aircraft will experience oscillations reducing to nil. A dynamically neutral aircraft will continue to oscillate around its original level, and dynamically unstable aircraft will experience increasing oscillations and displacement from its original level.
Dynamic stability is caused by damping. If damping is too great, the aircraft will be less responsive and less manoeuvrable.
Decreasing phugoid
In aviation, a phugoid or fugoid is an aircraft motion in which the vehicle pitches up and climbs, and then pitches down and descends, accompanied by speeding up and slowing down as it goes "downhill" and "uphill". This is one of the basic flig ...
(long-period) oscillations can be achieved by building a smaller stabilizer on a longer tail, and by shifting the center of gravity to the rear.
An aircraft that is not statically stable cannot be dynamically stable.
Analysis
Near the cruise condition most of the lift force is generated by the wings, with ideally only a small amount generated by the fuselage and tail. We may analyse the longitudinal static stability by considering the aircraft in equilibrium under wing lift, tail force, and weight. The moment equilibrium condition is called trim
Trim or TRIM may refer to:
Cutting
* Cutting or trimming small pieces off something to remove them
** Book trimming, a stage of the publishing process
** Pruning, trimming as a form of pruning often used on trees
Decoration
* Trim (sewing), or ...
, and we are generally interested in the longitudinal stability of the aircraft about this trim condition.
Equating force
In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
s in the vertical direction:
:
where W is the weight, is the wing lift and is the tail force.
For a thin airfoil at low angle of attack
In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is m ...
, the wing lift is proportional to the angle of attack:
:
where is the wing area is the (wing) lift coefficient
In fluid dynamics, the lift coefficient () is a dimensionless quantity that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area. A lifting body is a foil or a com ...
, is the angle of attack. The term is included to account for camber, which results in lift at zero angle of attack. Finally is the dynamic pressure
In fluid dynamics, dynamic pressure (denoted by or and sometimes called velocity pressure) is the quantity defined by:Clancy, L.J., ''Aerodynamics'', Section 3.5
:q = \frac\rho\, u^2
where (in SI units):
* is the dynamic pressure in pascals ( ...
:
:
where is the air density
The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature a ...
and is the speed.
Trim
The force from the tailplane is proportional to its angle of attack, including the effects of any elevator deflection and any adjustment the pilot has made to trim-out any stick force. In addition, the tail is located in the flow field of the main wing, and consequently experiences downwash
In aeronautics, downwash is the change in direction of air deflected by the aerodynamic action of an airfoil, wing, or helicopter rotor blade in motion, as part of the process of producing lift.Crane, Dale: ''Dictionary of Aeronautical Terms, thir ...
, reducing its angle of attack.
In a statically stable aircraft of conventional (tail in rear) configuration, the tailplane
A tailplane, also known as a horizontal stabiliser, is a small lifting surface located on the tail (empennage) behind the main lifting surfaces of a fixed-wing aircraft as well as other non-fixed-wing aircraft such as helicopters and gyroplane ...
force may act upward or downward depending on the design and the flight conditions.[p.19]
http://www.flightglobal.com/pdfarchive/view/1985/1985%20-%200562.html p.2
p.21
/ref> In a typical canard aircraft both fore and aft planes are lifting surfaces. The fundamental requirement for static stability is that the aft surface must have greater authority (leverage) in restoring a disturbance than the forward surface has in exacerbating it. This leverage is a product of moment arm from the center of gravity and surface area. Correctly balanced in this way, the partial derivative of pitching moment with respect to changes in angle of attack will be negative: a momentary pitch up to a larger angle of attack makes the resultant pitching moment tend to pitch the aircraft back down. (Here, pitch is used casually for the angle between the nose and the direction of the airflow; angle of attack.) This is the "stability derivative" d(M)/d(alpha), described below.
The tail force is, therefore:
:
where is the tail area, is the tail force coefficient, is the elevator deflection, and is the downwash angle.
A canard aircraft may have its foreplane rigged at a high angle of incidence, which can be seen in a canard catapult glider from a toy store; the design puts the c.g. well forward, requiring nose-up lift.
Violations of the basic principle are exploited in some high performance "relaxed static stability" combat aircraft to enhance agility; artificial stability is supplied by active electronic means.
There are a few classical cases where this favorable response was not achieved, notably in T-tail configurations. A T-tail airplane has a higher horizontal tail that passes through the wake of the wing later (at a higher angle of attack) than a lower tail would, and at this point the wing has already stalled and has a much larger separated wake. Inside the separated wake, the tail sees little to no freestream and loses effectiveness. Elevator control power is also heavily reduced or even lost, and the pilot is unable to easily escape the stall. This phenomenon is known as 'deep stall
In fluid dynamics, a stall is a reduction in the lift coefficient generated by a foil as angle of attack increases.Crane, Dale: ''Dictionary of Aeronautical Terms, third edition'', p. 486. Aviation Supplies & Academics, 1997. This occurs when t ...
'.
Taking moments about the center of gravity
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weight function, weighted relative position (vector), position of the distributed mass sums to zero. Thi ...
, the net nose-up moment is:
:
where is the location of the center of gravity behind the aerodynamic center
In aerodynamics, the torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift and net drag applied at some point on the airfoil, and a separate net pitching moment about that point whose magnitude ...
of the main wing, is the tail moment arm.
For trim, this moment must be zero. For a given maximum elevator deflection, there is a corresponding limit on center of gravity position at which the aircraft can be kept in equilibrium. When limited by control deflection this is known as a 'trim limit'. In principle trim limits could determine the permissible forwards and rearwards shift of the centre of gravity, but usually it is only the forward cg limit which is determined by the available control, the aft limit is usually dictated by stability.
In a missile context 'trim limit' more usually refers to the maximum angle of attack, and hence lateral acceleration which can be generated.
Static stability
The nature of stability may be examined by considering the increment in pitching moment with change in angle of attack at the trim condition. If this is nose up, the aircraft is longitudinally unstable; if nose down it is stable. Differentiating the moment equation with respect to :
:
Note: is a stability derivative.
It is convenient to treat total lift as acting at a distance h ahead of the centre of gravity, so that the moment equation may be written:
:
Applying the increment in angle of attack:
:
Equating the two expressions for moment increment:
:
The total lift is the sum of and so the sum in the denominator can be simplified and written as the derivative of the total lift due to angle of attack, yielding:
:
Where c is the mean aerodynamic chord
In aeronautics, the chord is an imaginary straight line joining the leading edge and trailing edge of an aerofoil. The chord length is the distance between the trailing edge and the point where the chord intersects the leading edge.L. J. Clan ...
of the main wing. The term:
:
is known as the tail volume ratio. Its coefficient, the ratio of the two lift derivatives, has values in the range of 0.50 to 0.65 for typical configurations. Hence the expression for h may be written more compactly, though somewhat approximately, as:
:
is known as the static margin. For stability it must be negative. (However, for consistency of language, the static margin is sometimes taken as , so that positive stability is associated with positive static margin.)
See also
* Directional stability
Directional stability is stability of a moving body or vehicle about an axis which is perpendicular to its direction of motion. Stability of a vehicle concerns itself with the tendency of a vehicle to return to its original direction in relation ...
* Flight dynamics
Flight dynamics in aviation and spacecraft, is the study of the performance, stability, and control of vehicles flying through the air or in outer space. It is concerned with how forces acting on the vehicle determine its velocity and attitude w ...
* Handling qualities Flying qualities is one of the three principal regimes in the science of flight test, which also includes performance and systems. Flying qualities involves the study and evaluation of the stability and control characteristics of an aircraft. They h ...
* Phugoid
In aviation, a phugoid or fugoid is an aircraft motion in which the vehicle pitches up and climbs, and then pitches down and descends, accompanied by speeding up and slowing down as it goes "downhill" and "uphill". This is one of the basic flig ...
References
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Aerodynamics
Aerospace engineering
Flight control systems
Aviation