Directional Stability and Control

Control and Stability 10

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

Definitions

The axis system of an aeroplane defines a positive yawing moment, N, as a moment about the normal 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:

The yawing moment coefficient, Cn, is based on the wing dimensions S and b as the wing is the characteristic surface of the aeroplane.

The sideslip angle relates the displacement of the aeroplane centre line from the relative airflow. Sideslip angle is provided the symbol β (beta) and is positive when the relative wind is displaced to the right of the aeroplane centre line. Figure 10.54 illustrates the definition of sideslip angle.

RELATIVE

AIRFLOW

A YAW TO THE LEFT GIVES

A SIDESLIP TO THE RIGHT

SIDESLIP

ANGLE

N, YAWING MOMENT

Figure 10.54 Sideslip angle (β)

The sideslip angle, β, is essentially the “directional angle of attack” of the aeroplane and is the primary reference in directional stability as well as lateral stability considerations. Static directional stability of the aeroplane is appreciated by response to sideslip.

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Figure 10.56

Figure 10.56 illustrates the fact that the instantaneous slope of the curve of Cn versus β will describe the static directional stability of the aeroplane.

•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 aeroplane.

Contribution of the Aeroplane Components.

Because the contribution of each component depends upon and is related to the others, it is necessary to study each separately.

Fuselage

The fuselage is destabilizing, Figure 10.57. It is an aerodynamic body and a condition of sideslip can be likened to an “angle of attack”, so that an aerodynamic side force is created. This side force acts through the fuselage aerodynamic centre (AC), which is close to the quarter-length point. If this aerodynamic centre is ahead of aircraft centre of gravity, as is usually the case, the effect is destabilizing.

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Figure 10.57

Dorsal andVentral Fins

To overcome the instability in the fuselage it is possible to incorporate into the overall design dorsal or ventral fins. A dorsal fin is a small aerofoil, of very low aspect ratio, mounted on top of the fuselage near the rear. A ventral fin is mounted below. Such fins are shown in Figure 10.58.

DORSAL FIN

FUSELAGE (Side View)

VENTRAL FIN

Figure 10.58

If the aircraft is yawed to the right, the dorsal and ventral fins will create a side force to the right. The line of action of this force is well aft of the aircraft CG, giving a yawing moment to the left (a stabilizing effect). However, at small angles of yaw they are ineffective.

LOW ASPECT RATIO

(or sweepback)

Figure 10.59

When fitted with dorsal and ventral fins, a fuselage which is unstable in yaw will remain unstable at low sideslip angles. Dorsal and ventral fins become more effective at relatively high sideslip angles. Due to their low aspect ratio, they do not tend to stall at any sideslip angle which an aircraft is likely to experience in service.

The effectiveness of dorsal and ventral fins increases with increasing sideslip angle, so that the combination of a fuselage with dorsal or ventral fin is stable at large sideslip angles.

While dorsal and ventral fins contribute in exactly the same way to directional static stability, a dorsal fin contributes positively to lateral static stability, while a ventral fin is destabilizing in this mode, as will be demonstrated later. For this reason, the dorsal fin is much more common.

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RELATIVE

AIRFLOW

TAIL MOMENT

ARM

CHANGE IN

FIN LIFT

Figure 10.61

Fin

The fin (vertical stabilizer) is the major source of directional stability for the aeroplane. As shown in Figure 10.61, in a sideslip the fin will experience a change in angle of attack. The change in lift (side force) on the fin creates a yawing moment about the centre of gravity which tends to yaw the aeroplane into the relative airflow. The magnitude of the fin contribution to static directional stability depends on both the change in fin lift and the fin moment arm. Clearly, the fin moment arm is a powerful factor.

The contribution of the fin to directional stability depends on its ability to produce changes in lift, or side force, for a given change in sideslip angle. The contribution of the fin is a direct function of its area. The required directional stability may be obtained by increasing the fin area. However, increased surface area has the obvious disadvantage of increased parasite drag.

The lift curve slope of the fin determines how sensitive the surface is to change in angle of attack. While it is desirable to have a high lift curve slope for the fin, a high aspect ratio surface is not necessarily practical or desirable - bending, lower stalling angle (Figure 10.59), hangar roof clearance, etc. The stall angle of the surface must be sufficiently great to prevent stall and subsequent loss of effectiveness at expected sideslip angles. (Sweepback or low aspect ratio increases the stalling angle of attack of the fin).

The flow field in which the fin operates is affected by other components of the aeroplane as well as power effects. The dynamic pressure at the fin could depend on the slipstream of a propeller or the boundary layer of the fuselage. Also, the local flow direction at the fin 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 fin to directional stability.

A high mounted tailplane (‘T’ - tail) makes the fin more effective by acting as an “end plate”.

The side force on the fin may still be relatively small compared to that on the fuselage, which is destabilizing, but because its line of action is far aft of the CG, the yawing moment it creates is relatively large and gives overall stability to the fuselage-fin combination. The principle behind the effect of the fin as a stabilizer is just the same as in the case of the dorsal or ventral fin. However, because it is much larger and, in particular, has a much higher aspect ratio, it is effective at low angles of sideslip. It remains effective until the angle of sideslip is such that the fin angle of attack approaches its stalling angle, but above this value, the side force on the fin decreases with increasing sideslip angle, and the fin ceases to be effective as a stabilizer. It is at this point that the dorsal or ventral fin becomes important. Because it stalls at a very much higher angle of attack, it takes over the stabilizing role of the fin at large angles of sideslip.

Wing and Nacelles

The contribution of the wing to static directional stability is usually small:

•The contribution of a straight wing alone is usually negligible.

•Sweepback produces a stabilizing effect, which increases with increase in CL (i.e. at lower IAS).

•Engine nacelles on the wings produce a contribution that will depend on such factors as their size and position and the shape of the wing planform. On a straight wing, they usually produce a destabilizing effect.

A swept wing provides a stable contribution depending on the amount of sweepback, but the contribution is relatively weak when compared with other components. Consider a sideslipping swept wing, as illustrated in Figure 10.62.

V

NORMAL

Figure 10.62

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The inclination of the forward, right, wing to the relative airflow is greater than that of the rearward wing, so there is more lift and, hence, more induced drag, on the right side, (the influence of increased lift on the forward wing will be explained when lateral static stability is considered). The result of this discrepancy in drag on the two sides of the wing is a yawing moment to the right, which tends to eliminate the sideslip. This is a stabilizing effect, and may be important if the sweepback angle is quite large.

Figure 10.63 illustrates a typical build-up of the directional stability of an aeroplane by separating the contribution of the fuselage and fin. As shown by the graph of Cn versus β, the contribution of the fuselage is destabilizing, but the instability decreases at large sideslip angles. The contribution of the fin alone is highly stabilizing up to the point where the surface begins to stall. The contribution of the fin must be large enough so that the complete aeroplane (wing-fuselage-fin combination) exhibits the required degree of stability.

AEROPLANE WITH

Figure 10.63

The dorsal fin has a powerful effect on preserving the directional stability at large angles of sideslip which would produce stall of the fin.

The addition of a dorsal fin to the aeroplane will reduce 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 fin is reduced which increases the stall angle for the surface.

By this twofold effect, the addition of the dorsal fin is a very useful device. The decreased lift curve slope of a swept-back fin will also decrease the tendency for the fin to stall at high sideslip angles.

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Power Effect

The effects of power on static directional stability are similar to the power effects on static longitudinal stability. The direct effect is confined to the normal force at the propeller plane and, of course, is destabilizing when the propeller is located ahead of the CG. In addition, the air in the slipstream behind a propeller spirals around the fuselage, and this results in a sidewash at the fin (from the left with a clockwise rotating propeller). The indirect effects of power induced velocities and flow direction changes at the fin (spiral slipstream effect) are quite significant for the propeller driven aeroplane and can produce large directional trim changes. As in the longitudinal case, the indirect effects are negligible for the jet powered aeroplane.

The contribution of the direct and indirect power effects to static directional stability is greatest for the propeller powered aeroplane and usually slight for the jet powered aeroplane. In either case, the general effect of power is destabilizing and the greatest contribution will occur at high power and low dynamic pressure.

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 of aeroplane. In 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.

Centre of Gravity Position

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

SIDESLIP ANGLE,

Figure 10.64

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High Angle of Attack

When the aeroplane is at a high angle of attack a decrease in static directional stability can be anticipated. As shown by Figure 10.64, a high angle of attack reduces the stable slope of the curve of Cn versus β. The decrease in static directional stability is due in great part to the reduction in the contribution of the fin. At high angles of attack, the effectiveness of the fin is reduced because of increase in the fuselage boundary layer at the fin location. The decay of directional stability with angle of attack is most significant for an aeroplane with sweepback since this configuration requires a high angle of attack to achieve high lift coefficients.

Figure 10.65

Ventral Fin

Ventral fins may be added as an additional contribution to directional stability, Figure 10.65. Landing clearance requirements may limit their size, require them to be retractable or require two smaller ventral fins to be fitted instead of one large one.

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

•high angle of sideslip

•high power at low airspeed

•high angle of attack

•high Mach number

The propeller powered aeroplane 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 transonic, jet powered aeroplane. In addition, the coupling of lateral and directional effects may require prescribed degrees of directional stability.