LATERAL STABILITY AND CONTROL

LATERAL STABILITY

The static lateral stability of an airplane involves consideration of rolling moments due

Revised January 1965

to sideslip. If an airplane has favorable rolling moment due to sideslip, a lateral displacement from wing level flight produces sideslip and the sideslip creates rolling moments tending to return the airplane 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 consid – rations of static lateral stability will involve only the relationship of rolling moments and sideslip.

DEFINITIONS. The axis system of an airplane 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 = CtqSb or

Q —J±- Li qSb

where

L = rolling moment, ft.-lbs., positive to the right

q = dynamic pressure, psf.

i’ = wing area, sq. ft.

b = wingspan, ft.

Cj=rolling moment coefficient, positive to the right

The angle of sideslip, /3, has been defined previously as the angle between the airplane centerline and the relative wind and is positive when the relative wind is to the right of the centerline.

The static lateral stability of an airplane can be illustrated by a graph of rolling moment coefficient, Ci, versus sideslip angle, j3, such as shown in figure 4.27. When the airplane is subject to a positive sideslip angle, lateral stability will be evident if a negative rolling moment coefficient results. Thus, when the relative wind comes from the right (+j9), a rolling moment to the left (—Cl) should be created which tends to roll the airplane to the left. Lateral stability will exist when the curve of Ci versus /3 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.

It is desirable to have lateral stability or favorable roll due to sideslip. However, the required magnitude of lateral stability is deter­mined by many factors. Excessive roll due to sideslip complicates crosswind takeoff and landing and may lead to undesirable oscil­latory coupling with the directional motion of the airplane. In addition, a high lateral sta­bility may combine with adverse yaw to hinder rolling performance. Generally, favorable han­dling qualities are obtained with a relatively light—or weak positive—lateral stability.

CONTRIBUTION OF THE AIRPLANE COMPONENTS. In order to appreciate the development of lateral stability in an airplane, each of the contribution components must be inspected. Of course, there will be interference between the components which will alter the contribution to stability of each component on the airplane.

The principal surface contributing to the lateral stability of an airplane is the wing. The effect of the geometric dihedral of a wing is a powerful contribution to lateral stability. As shown in figure 4.28, a wing with 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 effect a rolling moment tending to raise the windward wing hence dihedral contributes a stable roll due to sideslip.

CONTRIBUTION OF VERTICAL TAIL

SIDESLIP CONTRIBUTES
ROLLING MOMENT

Since wing 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 an equivalent amount of “effective dihedral” or “dihedral effect.”

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 stability of the com­bination. A wing located at the mid wing position will generally exhibit a dihedral effect no different from that of the wing alone. A low wing location on the fuselage may con­tribute an effect equivalent to 3° or 4° of nega­tive dihedral while a high wing location may contribute a positive dihedral of 2° or 3°. The magnitude of dihedral effect contributed by vertical position of the wing is large and may necessitate a noticeable dihedral angle for the low wing configuration.

The contribution of sweepback to dihedral ef­fect is important because of the nature of the contribution. As shown in figure 4.28, the swept wing in a sideslip has the wing into wind operating with an effective decrease in sweepback while the wing out of the wind is operating with an effective increase in sweepback. 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. In this manner the swept back wing would contribute a positive dihedral effect and the swept forward wing would contribute a negative dihedral effect.

The unusual nature of the contribution of sweepback to dihedral effect is that the con­tribution is proportional to the wing lift coefficient as well as the angle of sweepback. It should be clear that the swept wing at zero lift will provide no roll due to sideslip since there is no wing lift to change. Thus, the dihedral effect due to sweepback is zero at zero lift and increases directly with wing lift coefficient. When the demands of high speed flight require a large amount of sweepback, the resulting configuration may have an excessive­ly high dihedral effect at low speeds (high CL) while the dihedral effect may be satisfactory in normal flight (low or medium CL).

The vertical tail of modern configurations can provide a significant—and, at times, un­desirable—contribution to the effective dihe­dral. If the vertical tail is large, the side force produced by sideslip may produce a noticeable rolling moment as well as the important yaw­ing moment contribution. Such an effect is usually small for the conventional airplane configuration but the modern high speed airplane configuration induces this effect to a great magnitude. It is difficult then to obtain a large vertical tail contribution to directional stability without incurring an additional con­tribution to dihedral effect.

The amount of effective dihedral necessary to produce satisfactory flying qualities varies greatly with the type and purpose of the air­plane, Generally, the effective dihedral should not be too great since high roll due to side­slip can create certain problems. Excessive dihedral effect can lead to “Dutch roll,” difficult rudder coordination in rolling maneu­vers, or place extreme demands for lateral control power during crosswind takeoff and landing. Of course, the effective dihedral should not be negative during the predominat­ing conditions of flight, e. g,, cruise, high speed, etc. If the airplane demonstrates satis­factory dihedral effect for these conditions of flight, certain exceptions can be considered when the airplane is in the takeoff and landing configuration. Since the effects of flaps and power are destablizing and reduce the dihedral effect, a certain amount of negative dihedral effect may be possible due to these sources.

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. 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 airplane but considerable for the propeller driven airplane. 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 airplane in the power approach or waveoff.

With certain exceptions during the condi­tions of landing and takeoff, 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.