Longitudinal stability
[1] 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.
[2] Longitudinal static stability refers to the aircraft's initial tendency on pitching.
Dynamic stability refers to whether oscillations tend to increase, decrease or stay constant.
[1] This means the aircraft will self-correct longitudinal (pitch) disturbances without pilot input.
[4]: 27 The longitudinal static stability of an aircraft depends on the location of its center of gravity relative to the neutral point.
[5][4] The distance between the center of gravity and the neutral point is defined as "static margin".
[6]: 92 If the center of gravity is forward of the neutral point, the static margin is positive.
[7]: 8 If the center of gravity is aft of the neutral point, the static margin is negative.
The operating handbook for every airplane specifies a range over which the center of gravity is permitted to move.
[5] Some aerobatic and fighter aircraft may have low or even negative stability to provide high manoeuvrability.
[9][10][5] An aircraft with low or negative static stability will typically have fly-by-wire controls with computer augmentation to assist the pilot.
[1] 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.
[12] 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.
In contrast, guided missiles usually have a negative static margin for increased maneuverability.
[3][11]: 588 Decreasing phugoid (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.
We may analyse the longitudinal static stability by considering the aircraft in equilibrium under wing lift, tail force, and weight.
In addition, the tail is located in the flow field of the main wing, and consequently experiences downwash, reducing its angle of attack.
In a statically stable aircraft of conventional (tail in rear) configuration, the tail-plane force may act upward or downward depending on the design and the flight conditions.
[14] In a typical canard aircraft both fore and aft planes are lifting surfaces.
This leverage is a product of moment arm from the center of gravity and surface area.
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.
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.
In a missile context 'trim limit' more usually refers to the maximum angle of attack, and hence lateral acceleration which can be generated.
The nature of stability may be examined by considering the increment in pitching moment with change in angle of attack at the trim condition.
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
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 of the main wing.
Its coefficient, the ratio of the two lift derivatives, has values in the range of 0.50 to 0.65 for typical configurations.
