DIRECTIONAL STABILITY AND CONTROL

DIRECTIONAL STABILITY

The directional stability of an airplane is essentially the “weathercock” stability and involves moments about the vertical axis and their relationship with yaw or sideslip angle. An airplane which has static directional sta­bility would tend to return to an equilibrium when subjected to some disturbance from equi­librium. Evidence of static directional sta­bility would be the development of yawing moments which tend to restore the airplane to equilibrium.

DEFINITIONS. The axis system of an air­plane will define a positive yawing moment, N, as a moment about the vertical axis which tends to rotate the nose to the right. As in other aerodynamic considerations, it is con­venient to consider yawing moments in the coefficient form so that static stability can be evaluated independent of weight, altitude, speed, etc. The yawing moment, N, is de­fined in the coefficient form by the following equation:

N = CnqSb or

where

N= yawing moment, ft.-lbs;

positive to the right q = dynamic pressure, psf T = wing area, sq. ft. b = wing span, ft.

C„ = yawing moment coefficient, positive to the right

The yawing moment coefficient, C„, is based on the wing dimensions. S’ and b as the wing is the characteristic surface of the airplane.

The yaw angle of an airplane relates the dis­placement of the airplane centerline from some reference azimuth and is assigned the short­, hand notation ф (psi). A positive yaw angle occurs when the nose of the airplane is dis­placed to the right of the azimuth direction. The definition of sideslip angle involves a sig­nificant difference. Sideslip angle relates the displacement of the airplane centerline from the relative wind rather than some reference azimuth. Sideslip angle is provided the short­hand notation /8 (beta) and is positive when the relative wind is displaced to the right of the airplane centerline. Figure 4.22 illustrates the definitions of sideslip and yaw angles.

The sideslip angle, /3, is essentially the di­rectional angle of attack of the airplane and is the primary reference in lateral stability as well as directional stability considerations. The yaw angle, ф, is a primary reference for wind tunnel tests and time history motion of an airplane. From the definitions there is no direct relationship between /3 and ф for an airplane in free flight, e. g., an airplane flown through a 360° turn has yawed 360° but side­slip may have been zero throughout the entire turn. Since the airplane has no directional sense, static directional stability of the air­plane is appreciated by response to sideslip.

The static dinctional stability of an airplane can be illustrated by a graph of yawing moment coefficient, C„} versus sideslip angle, such as shown in figure 4.22. When the airplane is subject to a positive sideslip angle, static direc­tional stability will be evident if a positive yawing moment coefficient results. Thus, when the relative wind comes from the right (+j3), a yawing moment to the right (+C.) should be created which tends to weathercock the airplane and return the nose into the wind. Static directional stability will exist when the curve of Cn versus (3 has a positive slope and the degree of stability will be a function of the slope of this curve. If the curve has zero slope, there is no tendency to return to equilibrium and neutral static directional stability exists. When the curve of Cn versus 0 has a negative slope, the yawing moments developed by side­slip tend to diverge rather than restore and static directional instability exists.

The final chart of figure 4.22 illustrates the fact that the instantaneous slope of the curve of Cn versus /3 will describe the static directional stability of the airplane. At small angles of sideslip a strong positive slope depicts strong directional stability. Large angles of sideslip produce zero slope and neutral stability. At very high sideslip the negative slope of the curve indicates directional instability. This decay of directional stability with increased sideslip is not an unusual condition. However, directional instability should not occur at the angles of sideslip of ordinary flight conditions.

Static directional stability must be in evi­dence for all the critical conditions of flight. Generally, good directional stability is a fun­damental quality directly affecting the pilots’ impression of an airplane.

CONTRIBUTION OF THE AIRPLANE COMPONENTS. The static directional sta­bility of the airplane is a result of contribution ofi each of the various airplane components. While the contribution of each component is somewhat dependent upon and related to other components, it is necessary to study each component separately.

The vertical tail is the primary source of directional stability for the airplane. As shown in figure 4.23, when the airplane is in a sideslip the vertical tail will experience a change in angle of attack. The change in lift—or side force—on the vertical tail creates a yawing moment about the center of gravity which tends to yaw the airplane into the relative wind. The magnitude of the vertical tail contribution to static directional stability then depends on the change in tail lift and the tail moment arm. Obviously, the tail moment arm is a powerful factor but essentially dic­tated by the major configuration properties of the airplane.

When the location of the vertical tail is set, the contribution of the surface to directional stability depends on its ability to produce changes in lift—or side force—with changes in sideslip. The surface area of the vertical tail is a powerful factor with the contribution of the vertical tail being a direct function of the area. When all other possibilities are ex­hausted, the required directional stability may be obtained by increases in tail area. How­ever, increased surface area has the obvious disadvantage of increased drag.

The lift curve slope of the vertical tail relates how sensitive the surface is to changes in angle of attack. While it is desirable to have a high lift curve slope for the vertical surface, a high aspect ratio surface is not necessarily practical or desirable. The stall

angle of the surface must be sufficiently great to prevent stall and subsequent loss of effec­tiveness at ordinary sideslip angles. The high Mach numbers of supersonic flight produces a decrease in lift curve slope with the consequent reduction in tail contribution to stability. In order to have sufficient directional stability at high Mach numbers, the typical supersonic configuration will exhibit relatively large vertical tail surfaces.

The flow field in which the vertical tail operates is affected by the other components of the airplane as well as power effects. The dynamic pressure at the vertical tail could depend on the slipstream of a propeller or the boundary layer of the fuselage. Also, the local flow direction at the vertical tail is in­fluenced by the wing wake, fuselage crossflow, induced flow of the horizontal tail, or the direction of slipstream from a propeller. Each of these factors must be considered as possibly affecting the contribution of the vertical tail to directional stability.

The contribution of the wing to static direc­tional stability is usually small. The swept wing provides a stable contribution depending on the amount of sweepback but the contribu­tion is relatively weak when compared with other components. –

The contribution of the fuselage and nacelles is of primary importance since these compo­nents furnish the greatest destabilizing in­fluence. The contribution of the fuselage and nacelles is similar to the longitudinal case with the exception that there is no large in­fluence of the induced flow field of the wing. The subsonic center of pressure of the fuselage will be located at or forward of the quarter- length point and, since the airplane c. g. is usually considerably aft of this point, the fuselage contribution will be destabilizing. However, at large angles of sideslip the large destabilizing contribution of the fuselage di­minishes which is some relief to the problem of maintaining directional stability at large displacements. The supersonic pressure. dis­tribution on the body provides a relatively greater aerodynamic force and, generally, a continued destabilizing influence.

Figure 4.23 illustrates a typical buildup of the directional stability of an airplane by separating the contribution of the fuselage and tail. As shown by the graph of C„ versus 0, the contribution of the fuselage is de­stabilizing but the instability decreases at large sideslip angles. The contribution of the vertical tail alone is highly stabilizing up to the point where the surface begins to stall. The contribution of the vertical tail must be large enough so that the complete airplane (wing-fuselage-tail combination) exhibits the required degree of stability.

The dorsal fin has a powerful effect on pre­serving the directional stability at large angles of sideslip which would produce stall of the vertical tail. The addition of a dorsal fin to the airplane will allay the decay of directional stability at high sideslip in two ways. The least obvious but most important effect is a large increase in the fuselage stability at large sideslip angles. In addition, the effective aspect ratio of the vertical tail is reduced which increases the stall angle for the surface. By this twofold effect, the addition of the dorsal fin is a v useful device.

Power effects on static directional stability are similar to the power effects on static longitudinal stability. The direct effects are confined to the normal force at the propeller plane or the jet inlet and, of course, are de­stabilizing when the propeller or inlet is located ahead of the c. g. The indirect effects of power induced velocities and flow direction changes at the vertical tail are quite significant for the propeller driven airplane and can pro­duce large directional trim changes. As in the lontitudinal case, the indirect effects are negligible for the jet powered airplane.

The contribution of the direct and indirect power effects to static directional stability is greatest for the propeller powered airplane and usually slight for the jet powered airplane. In either case, the general effect of power is

EFFECT OF RUDDER FLOAT ON STATIC
DIRECTIONAL STABILITY

destabilizing and the greatest contribution will occur at high power and low dynamic pressure as during a waveoff.

As in the case of longitudinal static stability, freeing the controls will reduce the effective­ness of the tail and alter the stability. While the rudder must be balanced to reduce control pedal forces, the rudder will tend to float or streamline and reduce the contribution of the vertical tail to static directional stability. The floating tendency is greatest at large angles of sideslip where large angles of attack for the vertical tail tend to decrease aerodynamic bal­ance. Figure 4.24 illustrates the difference be­tween rudder-fixed and rudder-free static di­rectional stability.

CRITICAL CONDITIONS. The most criti­cal conditions of static directional stability are usually the combination of several separate effects. The combination which produces the most critical condition is much dependent upon the type and mission of the airplane. Tn addi­tion, there exists a coupling of lateral and di­rectional effects such that the required degree of static directional stability may be deter­mined by some of these coupled conditions.

Center of gravity position has a relatively negligible effect on static directional stability. The usual range of c. g. position on any air­plane is set by the linits of longitudinal stability and control. Within this limiting range of c. g. position, no significant changes take place in the contribution of the vertical tail, fuselage, nacelles, etc. Hence, the static directional stability is essentially unaffected by the varia­tion of c. g. position within the longitudinal limits.

When the airplane is at a high angle of attack a decrease in static directional stability can be anticipated. As shown by the second chart of figure 4.24, a high angle of attack reduces the stable slope of the curve of Cn versus 0. The decrease in static directional stability is due in great part to the reduction in the contribution of the vertical tail. At high angles of attack, the effectiveness of the vertical tail is reduced because of increase in the fuselage boundary layer at the vertical tail location. The decay of directional stability with angle of attack is most significant for the low aspect ratio air­plane with sweepback since this configuration requires such high angles of attack to achieve high lift coefficients. Such decay in directional stability can have a profound effect on the re­sponse of the airplane to adverse yaw and spin characteristics.

High Mach numbers of supersonic flight reduce the contribution of the vertical tail to direc­tional stability because of the reduction of lift curve slope with Mach number. The third chart of figure 4.24 illustrates the typical decay of directional stability with Mach number. To produce the required directional stability at high Mach numbers, a very large vertical tail area may be necessary. Ventral fins may be added as an additional contribution to direc­tional stability but landing clearance require­ments may limit their size or require the fins to be retractable.

Hence, the most critical demands of static directional stability will occur from some combination of the following effects:

(1) high angle of sideslip

(2) high power at low airspeed

0) high angle of attack

(4) high Mach number The propeller powered airplane may have such considerable power effects that the critical conditions may occur at low speed while the effect of high Mach numbers may produce the critical conditions for the typical supersonic airplane. In addition, the coupling of lateral and directional effects may require prescribed degrees of directional stability.