Control and Stability of Aircraft

One of the key factors in the Wright brothers’ achievement of building the first heavier-than-air aircraft was their insight that a functional airplane would require a mastery of three disciplines:

1. Lift
2. Propulsion
3. Control

Whereas the first two had been studied to some success by earlier pioneers such as Sir George Cayley, Otto Lilienthal, Octave Chanute, Samuel Langley and others, the question of control seemed to have fallen by the wayside in the early days of aviation. Even though the Wright brothers build their own little wind tunnel to experiment with different airfoil shapes (mastering lift) and also built their own lightweight engine (improving propulsion) for the Wright flyer, a bigger innovation was the control system they installed on the aircraft.

Fundamentally, an aircraft manoeuvres about its centre of gravity and there are three unique axes about which the aircraft can rotate:

1. The longitudinal axis from nose to tail, also called the axis of roll, i.e. rolling one wing up and one wing down.
2. The lateral axis from wing tip to wing tip, also called the axis of pitch, i.e. nose up or nose down.
3. The normal axis from the top of the cabin to the bottom of landing gear, also called the axis of yaw, i.e. nose rotates left or right.

In a conventional aircraft we have a horizontal elevator attached to the tail to control the pitch. Second, a vertical tail plane features a rudder (much like on a boat) that controls the yawing. Finally, ailerons fitted to the wings can be used to roll the aircraft from side to side. In each case, a change in attitude of the aircraft is accomplished by changing the lift over one of these control surfaces.
For example:

1. Moving the elevator down increases the effective camber across the horizontal tail plane, thereby increasing the aerodynamic lift at the rear of the aircraft and causing a nose-downward moment about the aircraft’s centre of gravity. Alternatively, an upward movement of the elevator induces a nose-up movement.
2. In the case of the rudder, deflecting the rudder to one side increases the lift in the opposite direction and hence rotates the aircraft nose in the direction of the rudder deflection.
3. In the case of ailerons, one side is being depressed while the other is raised to produce increased lift on one side and decreased lift on the other, thereby rolling the aircraft.

In the early 20th century the notion of using an elevator and rudder to control pitching and yawing were appreciated by aircraft pioneers. However, the idea of banking an aircraft to control its direction was relatively new. This is fundamentally what the Wright brothers understood. Looking at the Wright Flyer from 1903 we can clearly see a horizontal elevator at the front and a vertical rudder at the back to control pitch and yaw. But the big innovation was the wing warping mechanism which was used to control the sideways rolling of the aircraft. Check out the video below to see the elevator, rudder and wing warping mechanisms in action.

Today, many other control systems are being used in addition to, or instead of, the conventional system outlined above. Some of these are:

1. Elevons – combined ailerons and elevators.
2. Tailerons – two differentially moving tailplanes.
3. Leading edge slats and trailing edge flaps – mostly for increased lift at takeoff and landing.

But ultimately the action of operation is fundamentally the same, the lift over a certain portion of the aircraft is changed, causing a moment about the centre of gravity.

Special Aileron Conditions
Two special conditions arise in the operation of the ailerons.

The first is known as adverse yaw. As the ailerons are deflected, one up and one down, the aileron pointing down induces more aerodynamic drag than the aileron pointing up. This induced drag is a function of the amount of lift created by the airfoil. In simplistic terms, an increase in lift causes more pronounced vortex shedding activity, and therefore a high-pressure area behind the wing, which acts as a net retarding force on the aircraft. As the downward pointing airfoil produces more lift, induced drag is correspondingly greater. This increased drag on the downward aileron (upward wing) yaws the aircraft towards this wing, which must be counterbalanced by the rudder. Aerodynamicists can counteract the adverse yawing effect by requiring that the downward pointing aileron deflects less than the upward pointing one. Alternatively, Frise ailerons are used, which employ ailerons with excessively rounded leading edges to increase the drag on the upward pointing aileron and thereby help to counteract the induced drag on the downward pointing aileron of the other wing. The problem with Frise ailerons is that they can lead to dangerous flutter vibrations, and therefore differential aileron movement is typically preferred.

The second effect is known as aileron reversal, which occurs under two different scenarios.

• At very low speeds with high angles of attack, e.g. during takeoff or landing, the downward deflection of an aileron can stall a wing, or at the least reduce the lift across the wing, by increasing the effective angle of attack past sustainable levels (boundary layer separation). In this case, the downward aileron produces the opposite of the intended effect.
• At very high airspeeds, the upward or downward deflection of an aileron may produce large torsional moments about the wing, such that the entire wing twists. For example, a downward aileron will twist the trailing edge up and leading edge down, thereby decreasing the angle of attack and consequently also the lift over that wing rather than increasing it. In this case, the structural designer needs to ensure that the torsional rigidity of the wing is sufficient to minimise deflections under the torsional loads, or that the speed at which this effect occurs is outside the design envelope of the aircraft.

Stability
What do we mean by the stability of an aircraft? Fundamentally we have to discern between the stability of the aircraft to external impetus, with and without the pilot responding to the perturbation. Here we will limit ourselves to the inherent stability of the aircraft. Hence the aircraft is said to be stable if it returns back to its original equilibrium state after a small perturbing displacement, without the pilot intervening. Thus, the aircraft’s response arises purely from the inherent design. At level flight we tend to refer to this as static stability. In effect the airplane is statically stable when it returns to the original steady flight condition after a small disturbance; statically unstable when it continues to move away from the original steady flight condition upon a disturbance; and neutrally stable when it remains steady in a new condition upon a disturbance. The second, and more pernicious type of stability is dynamic stability. The airplane may converge continuously back to the original steady flight state; it may overcorrect and then converge to the original configuration in a oscillatory manner; or it can diverge completely and behave uncontrollably, in which case the pilot is well-advised to intervene. Static instability naturally implies dynamic instability, but static stability does not generally guarantee dynamic stability.

Longitudinal/Directional stability
By longitudinal stability we refer to the stability of the aircraft around the pitching axis. The characteristics of the aircraft in this respect are influenced by three factors:

1. The position of the centre of gravity (CG). As a rule of thumb, the further forward (towards the nose) the CG, the more stable the aircraft with respect to pitching. However, far-forward CG positions make the aircraft difficult to control, and in fact the aircraft becomes increasingly nose heavy at lower airspeeds, e.g. during landing. The further back the CG is moved the less statically stable the aircraft becomes. There is a critical point at which the aircraft becomes neutrally stable and any further backwards movement of the CG leads to uncontrollable divergence during flight.
2. The position of the centre of pressure (CP). The centre of pressure is the point at which the aerodynamic lift forces are assumed to act if discretised onto a single point. Thus, if the CP does not coincide with the CG, pitching moments will naturally be induced about the CG. The difficulty is that the CP is not static, but can move during flight depending on the angle of incidence of the wings.
3. The design of the tailplane and particularly the elevator. As described previously, the role of the elevator is to control the pitching rotations of the aircraft. Thus, the elevator can be used to counter any undesirable pitching rotations. During the design of the tailplane and aircraft on a whole it is crucial that the engineers take advantage of the inherent passive restoring capabilities of the elevator. For example, assume that the angle of incidence of the wings increases (nose moves up) during flight as a result of a sudden gust, which gives rise to increased wing lift and a change in the position of the CP. Therefore, the aircraft experiences an incremental change in the pitching moment about the CG given by

At the same time, the elevator angle of attack also increases due to the nose up/tail down perturbation. Hence, the designer has to make sure that the incremental lift of the elevator multiplied by its distance from the CG is greater than the effect of the wings, i.e.

As a result the interplay between CP and CG, tailplane design greatly influences the degree of static pitching stability of an aircraft. In general, due to the general tear-drop shape of an aircraft fuselage, the CP of an aircraft is typically ahead of it’s CG. Thus, the lift forces acting on the aircraft will always contribute some form of destabilising moment about the CG. It is mainly the job of the vertical tailplane (the fin) to provide directional stability, and without the fin most aircraft would be incredibly difficult to fly if not outright unstable.

Lateral Stability
By lateral stability we are referring to the stability of the aircraft when rolling one wing down/one wing up, and vice versa. As an aircraft rolls and the wings are no longer perpendicular to the direction of gravitational acceleration, the lift force, which acts perpendicular to the surface of the wings, is also no longer parallel with gravity. Hence, rolling an aircraft creates both a vertical lift component in the direction of gravity and a horizontal side load component, thereby causing the aircraft to sideslip. If these sideslip loads contribute towards returning the aircraft to its original configuration, then the aircraft is laterally stable. Two of the more popular methods of achieving this are:

1. Upward-inclined wings, which take advantage of the dihedral effect. As an aircraft is disturbed laterally, the rolling action to one side results in a greater angle of incidence on the downward-facing wing than the upward-facing one. This occurs because the forward and downward motion of the wing is equivalent to a net increase in angle of attack, whereas the forward and upward motion of the other wing is equivalent to a net decrease. Therefore, the lift acting on the downward wing is greater than on the upward wing. This means that as the aircraft starts to roll sideways, the lateral difference in the two lift components produces a moment imbalance that tends to restore the aircraft back to its original configuration. This is in effect a passive controlling mechanism that does not need to be initiated by the pilot or any electronic stabilising control system onboard. The opposite destabilising effect can be produced by downward pointing anhedral wings, but conversely this design improves manoeuvrability.
   

   The Dihedral Effect with Sideslip. Figure from (1).

2. Swept back wings. As the aircraft sideslips, the downward-pointing wing has a shorter effective chord length in the direction of the airflow than the upward-pointing wing. The shorter chord length increases the effective camber (curvature) of the lower wing and therefore leads to more lift on the lower wing than on the upper. This results in the same restoring moment discussed for dihedral wings above.
   

   The Sweepback Effect of Shortened Chord. Figure from (1).

It is worth mentioning that the anhedral and backward wept wings can be combined to reach a compromise between stability and manoeuvrability. For example, an aircraft may be over-designed with heavily swept wings, with some of the stability then removed by an anhedral design to improve the manoeuvrability.

Interaction of Longitudnal/Directional and Lateral Stability
As described above, movement of the aircraft in one plane is often coupled to movement in another. The yawing of an aircraft causes one wing to move forwards and the other backwards, and thus alters the relative velocities of the airflow over the wings, thereby resulting in differences in the lift produced by the two wings. The result is that yawing is coupled to rolling. These interaction and coupling effects can lead to secondary types of instability.

For example, in spiral instability the directional stability of yawing and lateral stability of rolling interact. When we discussed lateral stability, we noted that the sideslip induced by a rolling disturbance produces a restoring moment against rolling. However, due to directional stability it also produces a yawing effect that increases the bank. The relative magnitude of the lateral and directional restoring effects define what will happen in a given scenario. Most aircraft are designed with greater directional stability, and therefore a small disturbance in the rolling direction tends to lead to greater banking. If not counterbalanced by the pilot or electronic control system, the aircraft could enter an ever-increasing diving turn.

Another example is the dutch roll, an intricate back-and-forth between yawing and rolling. If a swept wing is perturbed by a yawing disturbance, the now slightly more forward-pointing wing generates more lift, exactly for the same argument as in the sideswipe case of shorter effective chord and larger effective area to the airflow. As a result, the aircraft rolls to the side of the slightly more backward-pointing wing. However, the same forward-pointing wing with higher lift also creates more induced drag, which tends to yaw the aircraft back in the opposite direction. Under the right circumstances this sequence of events can perpetuate to create an uncomfortable wobbling motion. In most aircrafts today, dampers in the automatic control system are installed to prevent this oscillatory instability.

In this post I have only described a small number of control challenges that engineers face when designing aircraft. Most aircraft today are controlled by highly sophisticated computer programmes that make loss of control or stability highly unlikely. Free unassisted “Flying-by-wire”, as it is called, is getting rarer and mostly limited to start and landing manoeuvres. In fact, it is more likely that the interface between human and machine is what will cause most system failures in the future.

References

(1) Richard Bowyer (1992). Aerodynamics for the Professional Pilot. Airlife Publishing Ltd., Shrewsbury, UK.