Longitudinal Stability

Longitudinal stability is stability in pitch. It decides whether an aeroplane, once trimmed, holds its angle of attack and speed when a gust or a brief control input disturbs it, and how the control forces tell the pilot that speed or load factor has changed. It is the one form of stability that can usually be studied on its own, because a pitching motion does not by itself cause roll or yaw.

Its main ingredients are the tailplane, the position of the centre of gravity (CG) relative to a point called the neutral point, and the behaviour of the elevator when the pilot lets go. Together they explain the forward and aft CG limits, the different feel of the same aeroplane at different loadings, and the two pitch oscillations, the phugoid and the short period, that every conventional aeroplane possesses. The general ideas of static and dynamic stability are set out in aircraft axes and stability fundamentals.

Static longitudinal stability

Static longitudinal stability is the initial tendency of an aeroplane, after a disturbance in pitch, to return to its trimmed angle of attack. Suppose an upward gust raises the angle of attack of both the wing and the tailplane:

• The wing's lift increases. The change can be taken to act at the wing's aerodynamic centre, near 25 % of the mean aerodynamic chord. When the CG lies behind that point, as it usually does, the extra lift pitches the nose further up. A wing on its own is therefore statically unstable in pitch.
• The tailplane's lift also changes, upwards. Acting on a long arm behind the CG, that change pitches the nose down, against the disturbance.

If the tailplane's nose-down moment exceeds the wing's nose-up moment, the aeroplane has positive static longitudinal stability. On a graph of pitching moment coefficient against angle of attack, a stable aeroplane shows a negative slope: a nose-up disturbance produces a nose-down moment. The tailplane's contribution grows with its area and its moment arm, which makes the horizontal stabiliser the primary source of pitch stability.

Most other parts of the aeroplane work against it:

• The fuselage is usually destabilising, because its own aerodynamic centre lies ahead of the CG.
• Downwash from the wing reduces the change in tailplane angle of attack for a given disturbance, weakening the tail's contribution. A T-tail placed above the downwash keeps more of it.
• A propeller ahead of the CG develops a force across its disc that grows with angle of attack, a destabilising effect that is greatest at high power and low airspeed.
• A thrust line below the CG makes the nose rise when power is increased.
• Flap increases the downwash at the tail and reduces the dynamic pressure there, and the usual net result is destabilising.

Because power and flap both erode stability, the least stable condition is often a powered approach or a go-around, and the neutral point in that configuration may be what sets the aft CG limit.

The tailplane and tail download

Stability and trim are separate questions. Stability depends on how the pitching moments change when the angle of attack changes; trim depends on whether they balance in the first place.

On a conventional aeroplane the wing's lift, taken at its aerodynamic centre, normally acts behind the CG, and a cambered wing also produces a nose-down pitching moment about that point. Lift and weight therefore form a nose-down couple. The tailplane balances it with a tailplane download, also called tail download or tail downforce, and normally flies at a negative angle of attack to produce it. In vertical equilibrium the wing must then support the weight plus the download, so the download costs induced drag, called trim drag, and raises the stalling speed. The further forward the CG, the larger the download, which is why a forward CG raises both the stall speed and the fuel burn (see centre of gravity).

The download is not what makes the aeroplane stable. Stability comes from the change in tail force when the angle of attack changes, and it exists whenever the CG is ahead of the neutral point, whatever the size or even the direction of the trimming load.

The download changes with configuration. Lowering flap increases the downwash angle at the tail, which makes the tail's angle of attack more negative and increases the download, a nose-up effect that opposes the nose-down moment of the flap itself. On a thin tailplane contaminated by ice, the same extra downwash can stall it, as described in tail configurations.

The trimming load is set either by an elevator held deflected by a trim tab or by a trimmable horizontal stabiliser, whose whole surface changes incidence while the elevator stays close to neutral. The second produces less trim drag and is the norm on jet transports.

CG, neutral point and static margin

Moving the CG forward lengthens the tailplane's moment arm and shortens the wing's, so stability increases; moving it aft does the reverse. Somewhere aft lies a CG position at which the stabilising and destabilising changes exactly cancel. That position is the neutral point (NP): the CG location at which the sum of the changes in tail and wing moments caused by a disturbance is zero, giving neutral static longitudinal stability. It can be pictured as the aerodynamic centre of the whole aeroplane, and it is the most aft CG position at which the aeroplane is not statically unstable.

The static margin is the distance the CG lies ahead of the neutral point, usually expressed as a percentage of the mean aerodynamic chord. It is the direct measure of static longitudinal stability: the larger the margin, the stronger the restoring moment. With the CG behind the neutral point the margin is negative, and a disturbance in pitch grows instead of dying away.

The CG limits keep the margin within a usable band:

• The aft CG limit lies some distance ahead of the neutral point to guarantee a minimum static margin, so in service the CG never reaches the neutral point. Spin recovery can also set the aft limit on light aeroplanes.
• The forward CG limit guarantees a minimum of controllability. The critical case is usually raising the nose in the landing flare, at low speed and in ground effect.

View full schematic

Stick-fixed and stick-free stability

The analysis so far assumes the elevator stays where it was. That is stick-fixed stability: the pilot holds the controls, or an irreversible powered control system holds the surface, and tailplane and elevator respond to a disturbance as one surface.

If the pilot lets go, an unbalanced elevator is free to trail with the airflow. When a disturbance raises the tailplane's angle of attack, the free elevator floats up towards the new relative airflow, which cancels part of the tail's change of lift. The tail becomes less effective, so stick-free static stability is less than stick-fixed stability and the stick-free neutral point lies ahead of the stick-fixed one. Horn balances, inset hinges and tabs change the floating tendency, and designers use them to keep an adequate stick-free margin.

Stick-free stability matters because it governs what the pilot feels. With positive stick-free stability a trimmed aeroplane needs a steady pull to hold a speed below the trim speed and a steady push to hold one above it, and when released it tends back towards the trim speed. On fully powered, irreversible controls the elevator cannot float; the forces come from an artificial feel system that senses dynamic pressure, and the feel and trim systems are designed to give the pilot the same message.

Stick force and stick force gradient

On a manual control the stick force is the force the pilot applies to balance the aerodynamic hinge moment on the surface, which is the surface force multiplied by its distance from the hinge line. That force is proportional to dynamic pressure, so for a given deflection the stick force rises with the square of the indicated airspeed.

The stick force gradient is the change in stick force per knot of speed away from the trim speed. It is how the pilot senses speed stability: a stable gradient means a pull below the trim speed and a push above it, so a speed change is felt before it is seen on the airspeed indicator. The gradient depends on the stick-free static margin; it becomes shallower as the CG moves aft and vanishes at the stick-free neutral point.

Where aerodynamics would spoil the gradient, systems restore it. A Mach trim system adds nose-up trim as Mach number increases, deliberately more than is needed simply to balance Mach tuck, so that the stick-force gradient stays stable (see high-speed flight). The Boeing 737's speed trim system improves speed stability at low weight, aft CG and high thrust when the autopilot is not engaged.

Stick force per g, manoeuvre point and manoeuvre margin

Stick force per g is the additional pull needed to increase the load factor by 1 g in a steady pull-up or turn. It tells the pilot how hard the wing is being loaded: too high and the aeroplane is tiring to manoeuvre, too low and a small pull can overstress it. The anti-servo tab on a stabilator is fitted partly to raise it.

In a steady pull-up the aeroplane is also rotating in pitch. The pitch rate increases the tailplane's angle of attack and adds a damping moment that the elevator must overcome, so more elevator, and more force, is needed for each g than static stability alone would suggest. The CG position at which the elevator angle per g (stick-fixed) or the stick force per g (stick-free) would fall to zero therefore lies behind the corresponding neutral point. That position is the manoeuvre point, and the distance of the CG ahead of it is the manoeuvre margin. As the CG moves aft the manoeuvre margin shrinks and so does the stick force per g, one of the reasons the aft limit is where it is.

Dynamic modes: phugoid and short period

After a disturbance in pitch, the motion of a conventional aeroplane combines two oscillations of very different character.

The short-period oscillation is a rapid pitching motion in which the angle of attack, the pitch rate and the load factor change sharply while speed and height stay almost constant. ATPL texts give its period as about one to two seconds or less. Because it changes the angle of attack so quickly, at a rate close to a pilot's reaction time, pilot inputs easily reinforce it, and certification requires it to be heavily damped. A pilot who meets it should relax or release the controls and let the damping work instead of chasing it. The damping comes mainly from the tailplane and decreases at high altitude.

The phugoid oscillation is a slow exchange of kinetic and potential energy. The nose drops, the aeroplane descends and gains speed; the extra speed gives extra lift, so it climbs, loses speed and the nose drops again. Pitch attitude, height and airspeed all vary noticeably, while the angle of attack stays almost constant. The period grows with true airspeed: ATPL texts quote one to two minutes, while in a light aeroplane it is tens of seconds. The phugoid may be only lightly damped, but it is so slow that the pilot or the autopilot removes it with small, unhurried corrections; a pilot often does so without noticing.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.