10 Stability and Control

Aeroplane Reference Axes

In order to visualize the forces and moments on the aircraft, it is necessary to establish a set of reference axes passing through the centre of gravity. Figure 10.4 illustrates a conventional right hand axis system.

The longitudinal axis passes through the CG from nose to tail. A moment about this axis is a rolling moment, L, and a roll to the right is a positive rolling moment.

The normal axis passes vertically through the CG at 90° to the longitudinal axis. A moment about the normal axis is a yawing moment, N, and a positive yawing moment would yaw the aircraft to the right.

The lateral axis is a line passing through the CG, parallel to a line passing through the wing tips. A moment about the lateral axis is a pitching moment, M, and a positive pitching moment is nose-up.

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Stability		Lateral Axis
and			Positive	Pitching
			Moment,
Control					Gravity
			M
					Centre Of
					Positive Yawing
		Positive			Moment,
					N
	Longitudinal	Rolling	Moment,
			L
	Axis
					Normal Axis
			Figure 10.4

Static Longitudinal Stability

Longitudinal stability is motion about the lateral axis. To avoid confusion, consider the axis about which the particular type of stability takes place. Thus, lateral stability is about the longitudinal axis (rolling), directional stability is about the normal axis (yawing) and longitudinal stability is about the lateral axis (pitching). Static longitudinal stability is considered first because it can be studied in isolation; in general, it does not interact with motions about the other two axes. Lateral and directional stability tend to interact (coupled motion), and these will be studied later.

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		Stability and Control		10
	•	An aircraft will exhibit static longitudinal stability if it tends to return towards the trim
		angle of attack when displaced by a gust OR a control input.
		• It is essential that an aircraft has positive static longitudinal stability. If it is stable, an
		aeroplane is safe and easy to fly since it seeks and tends to maintain a trimmed condition
		of flight. It also follows that control deflections and control “feel” (stick force) must be
		logical, both in direction and magnitude.
	•	If the aircraft is neutrally stable, it tends to remain at any displacement to which it is
		disturbed.
		• Neutral static longitudinal stability usually defines the lower limit of aeroplane stability
		since it is the boundary between stability and instability. The aeroplane with neutral
		static stability may be excessively responsive to controls and the aircraft has no tendency
		to return to trim following a disturbance - generally, this would not be acceptable.
	•	The aircraft which is unstable will continue to pitch in the disturbed direction until the	10
		displacement is resisted by opposing control forces.		Control
		• The aeroplane with negative static longitudinal stability is inherently divergent from any
				and
		intended trim condition. If it is at all possible to fly the aircraft, it cannot be trimmed and
				Stability
		of attitude and airspeed - clearly, this would be totally unacceptable.
		illogical control forces and deflections are required to provide equilibrium with a change

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10 Stability and Control

For the study of stability it is convenient to consider the changes in magnitude of lift force due to changes in angle of attack, acting through a stationary point, the aerodynamic centre (AC). It will be remembered that the location of the AC is at the quarter chord (or 25% aft of the leading edge). It should be noted that the pitching moment about the AC is negative (nosedown) and that this negative (nose-down) pitching moment about the AC does not change with changes in angle of attack. Figure 10.5.

		L 1
1	M
	AC	CP
10	d1
ControlandStability					L 2
		2		M
				AC	CP
				d2
	MOMENT (M) REMAINS THE SAME AT "NORMAL" ANGLES OF ATTACK BECAUSE
	L 1 × d1 at	α1	=	L2 × d2 at α2

Figure 10.5 Aerodynamic centre (AC)

The pitching moment about the AC remains constant as the angle of attack is increased because the magnitude of the lift force increases but acts through a smaller arm due to the CP moving forward. It is only at the AC (25% chord) that this will occur. If a point in front of, or to the rear of the AC were considered, the pitching moment would change with angle of attack.

For the study of stability, we will consider the lift to act at the AC. The AC is a stationary point located at the 25% chord only when the airflow is subsonic.

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Stability and Control 10

L

L

x

Flight	AC	wing
Path

Momentary Relative Airflow due to Gust

Figure 10.6 A wing alone is unstable

A wing considered alone is statically unstable because the AC is in front of the CG, Figure 10.6. A vertical gust will momentarily increase the angle of attack and increase lift (ΔL), which, when multiplied by arm ‘x’, will generate a positive (nose-up) pitching moment about the CG. This will tend to increase the angle of attack further, an unstable pitching moment. The wing on its own would rotate nose-up about the CG, Figure 10.7.

	L
		AN AIRCRAFT ROTATES
L		AROUND ITS CG

AC x CG

UNSTABLE (NOSE-UP)

PITCHING MOMENT

ABOUT THE CG

Figure 10.7

Now consider a wing together with a tailplane. The tailplane is positioned to generate a stabilizing pitching moment about the aircraft CG. The same vertical gust will increase the angle of attack of the tailplane and increase tailplane lift (ΔLt), which, when multiplied by arm ‘y’, will generate a negative (nose-down) pitching moment about the aircraft CG.

Stability and Control 10

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10 Stability and Control

If the tail moment is greater than the wing moment, the sum of the moments will not be zero and the resultant nose-down moment will give an angular acceleration about the CG. The nosedown angular acceleration about the CG will return the aircraft towards its original position of equilibrium. The greater the tail moment relative to the wing moment, the greater the rate of acceleration towards the original equilibrium position. (Too much angular acceleration is not good).

			L
		L		x	y
				AIRCRAFT	CG		Lt
	Flight		AC				L t
10	Path			wing
							AC tail
Stability
	Momentary		Relative Airflow
and	due to Gust				Momentary Relative Airflow
Control					due to Gust
		=	Change in angle of attack due to gust		L t	=	Tailplane lift
	AC	=	Aerodynamic Centre		L t	=	Change in tailplane lift
	L	=	Wing lift		x	=	Arm from wing AC to aircraft CG
	L	=	Change in wing lift		y	=	Arm from tailplane AC to aircraft CG

Figure 10.8

There are two moments to consider: the wing moment and the tail moment. The wing moment is a function of the change in wing lift multiplied by arm ‘x’. The tail moment is a function of the change in tailplane lift multiplied by arm ‘y’, Figure 10.8. The length of both arms is dependent upon CG position. If the CG is considered in a more forward position, the tail arm is larger and the wing arm is smaller. A more forward CG position increases static longitudinal stability.

If the nose-down (negative) tail moment is greater than the nose-up (positive) wing moment, the aircraft will have static longitudinal stability.

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