Stability and Control 10

Longitudinal Control

To be satisfactory, an aeroplane must have adequate controllability as well as adequate stability. An aeroplane with high static longitudinal stability will exhibit great resistance to displacement from equilibrium. Hence, the most critical conditions of controllability will occur when the aeroplane has high static stability, i.e. the lower limits of controllability will set the upper limits of static stability. (Fwd. CG limit).

There are three principal conditions of flight which provide the critical requirements of longitudinal control power (manoeuvring, take-off and landing). Any one or combination of these conditions can determine the overall longitudinal control power and set a limit to the forward CG position.

		10% MAC
	MAXIMUM	18% MAC	10
UP	DEFLECTION	MOST FORWARD	Control
		CG FOR MANOEUVRING
		CONTROLLABILITY
	20% MAC		and
		30% MAC
			Stability
		CL
DOWN	CG	C LMAX
	POSITION

Figure 10.43

Manoeuvring Control Requirement

The aeroplane should have sufficient longitudinal control power to attain the maximum usable lift coefficient or the limit load factor during manoeuvres. As shown in Figure 10.43, forward movement of the CG increases the longitudinal stability of an aeroplane and requires larger control deflections to produce changes in trim lift coefficient. For the example shown, the maximum effective deflection of the elevator is not capable of trimming the aeroplane at CLMAX for CG positions ahead of 18 percent MAC.

This particular control requirement can be most critical for an aeroplane in supersonic flight. Supersonic flight is usually accompanied by large increases in static longitudinal stability (due to aft CP movement) and a reduction in the effectiveness of control surfaces. In order to cope with these trends, powerful all-moving surfaces must be used to attain limit load factor or maximum usable CL in supersonic flight. This requirement is so important that once satisfied, the supersonic configuration usually has sufficient longitudinal control power for all other conditions of flight.

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Take-off Control Requirement

At take-off, the aeroplane must have sufficient elevator control power to assume the take-off attitude prior to reaching take-off speed.

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LIFT

TAIL

LOAD

ROLLING FRICTION

WEIGHT

Figure 10.44

Figure 10.44 illustrates the principal forces acting on an aeroplane during take-off roll. When the aeroplane is in the three point attitude at some speed less than the stall speed, the wing lift will be less than the weight of the aeroplane. As the elevators must be capable of rotating the aeroplane to the take-off attitude, the critical condition will be with zero load on the nose wheel and the net of lift and weight supported on the main gear.

Rolling friction resulting from the normal force on the main gear creates an adverse nose-down moment. Also, the CG ahead of the main gear contributes a nose-down moment. To balance these two nose-down moments, the horizontal tail must be capable of producing a nose-up moment big enough to attain the take-off attitude at the specified speed.

The propeller aeroplane at take-off power may induce considerable slipstream velocity at the horizontal tail which can provide an increase in the efficiency of the surface. The jet aeroplane does not experience a similar magnitude of this effect since the induced velocities from the jet are relatively small compared to the slipstream velocities from a propeller.

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Landing Control Requirement

At landing, the aeroplane must have sufficient control power to ensure adequate control at specified landing speeds. The most critical requirement will exist when the CG is in the most forward position, flaps are fully extended, and power is set at idle. This configuration will provide the most stable condition which is most demanding of controllability.

The landing control requirement has one particular difference from the manoeuvring control requirement of free flight. As the aeroplane approaches the surface, there will be a change in the three-dimensional flow over the aeroplane due to ground effect. A wing in proximity to the ground plane will experience a decrease in tip vortices and downwash at a given lift coefficient. The decrease in downwash at the tail tends to increase the static stability and produce a nosedown moment from the reduction in down load on the tail. Thus, the aeroplane just off the runway surface, Figure 10.45, will require additional control deflection to trim at a given lift coefficient, and the landing control requirement may be critical in the design of longitudinal control power.

REDUCED DOWNWASH

DUE TO GROUND EFFECT

Figure 10.45

As an example of ground effect, a typical propeller powered aeroplane may require as much as 15° more up elevator to trim at CLMAX in ground effect than in free flight.

In some cases the effectiveness of the elevator is adversely affected by the use of trim tabs.

If trim is used to excess in trimming stick forces, the effectiveness of the elevator may be reduced which would hinder landing or take-off control.

Each of the three principal conditions requiring adequate longitudinal control are critical for high static stability. If the forward CG limit is exceeded, the aeroplane may encounter a deficiency of controllability in any of these conditions.

The forward CG limit is set by the minimum permissible controllability.

The aft CG limit is set by the minimum permissible stability.

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Dynamic Stability

Control and Stability 10

While static stability is concerned with the initial tendency of an aircraft to return to equilibrium, dynamic stability is defined by the resulting motion with time. If an aircraft is disturbed from equilibrium, the time history of the resulting motion indicates its dynamic stability. In general, an aircraft will demonstrate positive dynamic stability if the amplitude of motion decreases with time. The various conditions of possible dynamic behaviour are illustrated in the following six history diagrams. The nonoscillatory modes shown in diagrams A, B and C depict the time histories possible without cyclic motion.

Initial

Disturbance

A SUBSIDENCE

(or Dead Beat Return)

TIME

(Positive Static)

(Positive Dynamic)

Figure 10.46 Chart A

Chart A illustrates a system which is given an initial disturbance and the motion simply subsides without oscillation; the mode is termed “subsidence” or “dead beat return.” Such a motion indicates positive static stability by the initial tendency to return to equilibrium and positive dynamic stability since the amplitude decreases with time.

B DIVERGENCE

TIME

(Negative Static)

(Negative Dynamic)

Figure 10.47 Chart B

Chart B illustrates the mode of “divergence” by a non-cyclic increase of amplitude with time. The initial tendency to continue in the displacement direction is evidence of static instability and the increasing amplitude is proof of dynamic instability.

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C

NEUTRAL STATIC STABILITY

(Neutral Static)

(Neutral Dynamic)

TIME

Figure 10.48 Chart C

Chart C illustrates the mode of pure neutral stability. If the original disturbance creates a displacement which then remains constant, the lack of tendency for motion and the constant amplitude indicate neutral static and neutral dynamic stability.

The oscillatory modes shown in diagrams D, E and F depict the time histories possible with cyclic motion. One feature common to each of these modes is that positive static stability is demonstrated by the initial tendency to return to equilibrium conditions. However, the resulting dynamic behaviour may be stable, neutral, or unstable.

D
DAMPED OSCILLATION
	TIME
(Positive	Static)
(Positive	Dynamic)

Figure 10.49 Chart D

Chart D illustrates the mode of a damped oscillation where the amplitude decreases with time. The reduction of amplitude with time indicates there is resistance to motion and that energy is being dissipated. Dissipation of energy or damping is necessary to provide positive dynamic stability.

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E
UNDAMPED OSCILLATION
(Positive	Static)
(Neutral	Dynamic)
TIME

Figure 10.50 Chart E

If there is no damping in the system, the mode of chart E is the result, an undamped oscillation. Without damping, the oscillation continues with no reduction of amplitude with time. While such an oscillation indicates positive static stability, neutral dynamic stability exists. Positive damping is necessary to eliminate the continued oscillation. As an example, a car with worn shock absorbers (or “dampers”) lacks sufficient dynamic stability and the continued oscillatory motion is both unpleasant and potentially dangerous. In the same sense, an aircraft must have sufficient damping to rapidly dissipate any oscillatory motion which would affect the safe operation of the aircraft. When natural aerodynamic damping cannot be obtained, artificial damping must be provided to give the necessary positive dynamic stability.

F

DIVERGENT OSCILLATION

(Positive	Static)
(Negative	Dynamic)
TIME

Figure 10.51 Chart F

Chart F illustrates the mode of a divergent oscillation. This motion is statically stable since it tends to return to the equilibrium position. However, each subsequent return to equilibrium is with increasing velocity such that amplitude continues to increase with time. Thus, dynamic instability exists.

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Divergent oscillation results when energy is supplied to the motion rather than dissipated by positive damping. An example of divergent oscillation occurs if a pilot unknowingly makes control inputs which are near the natural frequency of the aeroplane in pitch; energy is added to the system, negative damping exists, and Pilot Induced Oscillation (PIO) results.

The existence of static stability does not guarantee the existence of dynamic stability. However, the existence of dynamic stability implies the existence of static stability.

IF AN AIRCRAFT IS STATICALLY UNSTABLE,

IT CANNOT BE DYNAMICALLY STABLE

Any aircraft must demonstrate the required degrees of static and dynamic stability. If the aircraft were allowed to have static instability with a rapid rate of divergence, it would be very difficult, if not impossible to fly. In addition, positive dynamic stability is mandatory in certain areas to prevent objectionable continued oscillations of the aircraft.

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