Stability and Control 10

Lateral Stability and Control

The static lateral stability of an aeroplane involves consideration of rolling moments due to sideslip. If an aeroplane has favourable rolling moment due to a sideslip, a lateral displacement from wing level flight produces a sideslip, and the sideslip creates a rolling moment tending to return the aeroplane to wing level flight. By this action, static lateral stability will be evident. Of course, a sideslip will produce yawing moments depending on the nature of the static directional stability, but the consideration of static lateral stability will involve only the relationship of rolling moments and sideslip.

Definitions

The axis system of an aeroplane defines a positive rolling, L, as a moment about the longitudinal axis which tends to rotate the right wing down. As in other aerodynamic considerations, it is convenient to consider rolling moments in the coefficient form so that lateral stability can be evaluated independent of weight, altitude, speeds, etc. The rolling moment, L, is defined in the coefficient form by the following equation:

L = Cl Q S b

or

Cl =	L
	Q S b

where:

L = rolling moment (positive to right)

Q = dynamic pressure

S = wing area

b = wingspan

Cl = rolling moment coefficient (positive to the right)

The angle of sideslip, β,has been defined previously as the angle between the aeroplane centre line and the relative wind and is positive when the relative wind is to the right of the centre line.

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Static Lateral Stability

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Static lateral stability can be illustrated by a graph of rolling moment coefficient, Cl, versus sideslip angle, β, such as shown in Figure 10.67. When the aeroplane is subject to a positive sideslip angle, lateral stability will be evident if a negative rolling moment coefficient results. Thus, when the relative airflow comes from the right (+β), a rolling moment to the left (-Cl) should be created which tends to roll the aeroplane to the left. Lateral stability will exist when the curve of Cl versus β has a negative slope and the degree of stability will be a function of the slope of this curve. If the slope of the curve is zero, neutral lateral stability exists; if the slope is positive, lateral instability is present.

RELATIVE AIRFLOW

l, ROLLING MOMENT

Figure 10.66

ROLLING MOMENT COEFFICIENT

Cl

UNSTABLE

NEUTRAL

SIDESLIP ANGLE,

STABLE

Figure 10.67

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It is desirable to have static lateral stability (favourable roll due to sideslip), Figure 10.68. However, the required magnitude of lateral stability is determined by many factors. Excessive roll due to sideslip complicates crosswind take-off and landing and may lead to undesirable oscillatory coupling with the directional motion of the aeroplane. In addition, high lateral stability may combine with adverse yaw to hinder rolling performance. Generally, good handling qualities are obtained with a relatively light, or weak positive, lateral stability.

STABLE ROLL DUE

TO SIDESLIP

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NEUTRAL

UNSTABLE ROLL

DUE TO SIDESLIP

Figure 10.68 Static lateral stability

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Contribution of the Aeroplane Components

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In order to appreciate the development of lateral stability in an aeroplane, each of the components which contribute must be inspected. There will be interference between the components, which will alter the contribution to stability of each component on the aeroplane.

EFFECTIVE INCREASE IN

LIFT DUE TO SIDESLIP

EFFECTIVE DECREASE IN

LIFT DUE TO SIDESLIP

Figure 10.69 Geometric dihedral

Wing

The principal surface contributing to the lateral stability of an aeroplane is the wing. The effect of *geometric dihedral is a powerful contribution to lateral stability.

As shown in Figure 10.69, a wing with geometric dihedral will develop stable rolling moments with sideslip. If the relative wind comes from the side, the wing into the wind is subject to an increase in angle of attack and develops an increase in lift. The wing away from the wind is subject to a decrease in angle of attack and develops a decrease in lift. The changes in lift gives a rolling moment tending to raise the into-wind wing, hence geometric dihedral contributes a stable roll due to sideslip.

Since geometric dihedral is so powerful in producing lateral stability it is taken as a common denominator of the lateral stability contribution of all other components. Generally, the contribution of wing position, flaps, power, etc., is expressed as “DIHEDRAL EFFECT”.

*Geometric Dihedral: The angle between the plane of each wing and the horizontal, when the aircraft is unbanked and level; positive when the wing lies above the horizontal, as in Figure 10.69. Negative geometric dihedral is used on some aircraft, and is known as anhedral.

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Wing Position

The contribution of the fuselage alone is usually quite small; depending on the location of the resultant aerodynamic side force on the fuselage.

However, the effect of the wing - fuselage - tail combination is significant since the vertical placement of the wing on the fuselage can greatly affect the combination. A wing located at the mid wing position will generally exhibit a “dihedral effect” no different from that of the wing alone.

Figure 10.70 illustrates the effect of wing position on static lateral stability.

•A low wing position gives an unstable contribution. The direction of relative airflow decreases the effective angle of attack of the wing into wind and increases the effective angle of attack of the wing out of wind - tending to increase the rolling moment.

•A high wing location gives a stable contribution. The direction of relative airflow increases the effective angle of attack of the wing into wind and decreases the effective angle of attack of the wing out of wind, tending to decrease the rolling moment.

SIDESLIP

HIGH WING POSITION

LOW WING POSITION

Figure 10.70 Wing - fuselage interference effect

The magnitude of “dihedral effect” contributed by the vertical position of the wing is large and may require a noticeable dihedral angle for the low wing configuration. A high wing position, on the other hand, usually requires no geometric dihedral at all.

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Sweepback

The contribution of sweepback to “dihedral effect” is important because of the nature of the contribution. As shown in Figure 10.71 and Figure 10.72, if the wing is at a positive lift coefficient, the wing into the wind has less sweep and an increase in lift, and the wing out of the wind has more sweep and a decrease in lift; a negative rolling moment will be generated, tending to roll the wings towards level. In this manner the swept-back wing contributes a positive “dihedral effect”. (A swept-forward wing would give a negative dihedral effect).

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INCREASED

EFFECTIVE

SWEEP

DECREASED

EFFECTIVE

SWEEP

Figure 10.71 The effect of sweepback

The contribution of sweepback to “dihedral effect” is proportional to the wing lift coefficient as well as the angle of sweepback. Because high speed flight requires a large amount of sweepback, an excessively high “dihedral effect” will be present at low speeds (high CL). An aircraft with a swept-back wing requires less geometric dihedral than a straight wing.

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		LEADING WING
		IN SIDESLIP
CL	DIFFERENCE IN
	LIFT ON THE
	TWO WINGS	ZERO
		SIDESLIP
		TRAILING WING
		IN SIDESLIP
0	HIGH
	SPEED
		LOW
		SPEED

Figure 10.72 Effect of speed on ‘Dihedral Effect’ of swept wing

The fin can provide a small “dihedral effect” contribution, Figure 10.73. If the fin is large, the side force produced by sideslip may produce a rolling moment as well as the important yawing moment contribution. The fin contribution to purely lateral static stability is usually very small.

SMALL STABILIZING

ROLLING MOMENT IN

SIDESLIP

RELATIVE AIRFLOW

Figure 10.73 Fin contribution

The ventral fin, being below the aircraft CG, has a negative influence on lateral static stability, as illustrated in Figure 10.74.

SMALL DESTABILIZING

ROLLING MOMENT

IN SIDESLIP

VENTRAL

FIN

RELATIVE AIRFLOW

Figure 10.74 Ventral fin contribution

Generally, the “dihedral effect” should not be too great since high roll due to sideslip can create certain problems.

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Excessive “dihedral effect” can lead to “Dutch roll” difficult rudder coordination in rolling manoeuvres, or place extreme demands for lateral control power during crosswind take-off and landing. If the aeroplane demonstrates satisfactory “dihedral effect” during cruise, certain exceptions can be tolerated when the aeroplane is in the take-off and landing configuration. Since the effects of flaps and power are destabilizing and reduce the “dihedral effect”, a certain amount of negative “dihedral effect” may be possible due to these sources.

REDUCED ARM

Figure 10.75 Partial span flaps reduce lateral stability

The deflection of flaps causes the inboard sections of the wing to become relatively more effective and these sections have a small spanwise moment arm, Figure 10.75. Therefore, the changes in wing lift due to sideslip occur closer inboard and the dihedral effect is reduced.

The effect of power on “dihedral effect” is negligible for the jet aeroplane but considerable for the propeller driven aeroplane. The propeller slipstream at high power and low airspeed makes the inboard wing sections much more effective and reduces the dihedral effect.

The reduction in “dihedral effect” is most critical when the flap and power effects are combined, e.g. the propeller driven aeroplane in a power-on approach.

With certain exceptions during the conditions of landing and take-off, the “dihedral effect” or lateral stability should be positive but light. The problems created by excessive “dihedral effect” are considerable and difficult to contend with. Lateral stability will be evident to a pilot by stick forces and displacements required to maintain sideslip. Positive stick force stability will be evident by stick forces required in the direction of the controlled sideslip.

Conclusion

The designer is faced with a dilemma. An aircraft is given sweepback to increase the speed at which it can operate, but a by-product of sweepback is static lateral stability. A swept-back wing requires much less geometric dihedral than a straight wing. If a requirement also exists for the wing to be mounted on top of the fuselage, an additional “dihedral effect”is present. A high mounted and swept-back wing would give excessive “dihedral effect”, so anhedral is used to reduce “dihedral effect” to the required level.

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