Roll with sideslip and directional stability

A common error is to assume that the term lateral stability satisfies the definition of stability, given in Section 8.3.1: namely that if an aircraft is disturbed by a gust (or by the pilot operating its pitch or yaw controls), then it is stable if it attempts to return to its previously trimmed condition. This definition would mean that it will pitch or yaw in such a way that it ends up pointing into the new wind, from whichever direction it is blowing. Clearly this implies rolling into the new wind as well, which is something to be prevented at all costs if a spiral dive is

to be avoided. The danger of the spiral dive — the original killer — is that rolling in the direction of the new wind leads to the nose dropping and speed building up. Unless the pilot acts quickly to correct the situation the aircraft may be overstressed. To be laterally stable the aeroplane must do the opposite, it must roll away from the wind.

Let us look at this in detail to understand how roll with sideslip and directional stability are mutually dependent. Imagine an aeroplane to be flying straight and level before meeting a lateral gust. The gust causes a change of angle of attack in the X—Y plane, as shown in Fig. 8.15.

Fig. 8.15 Stabilizing and destabilizing moments of fin and fuselage in yaw.

The side-force generated by the fuselage usually acts ahead of the CG and is destabilizing. For the aircraft to possess weathercock stability (an early term for directional stability) the side-force generated by the fin and rudder acting as one unit must be powerful enough to overcome the yawing moment of the fuselage side-force.

Ideally the yaw should be corrected in such a way that the heading of the aeroplane is unchanged in space. However, if the nose merely swings round to point into the relative wind, then the heading will be altered by an angle roughly equivalent to the angle of yaw. In yawing the outer wing travels faster than the inner wing and generates more lift, so that (in this particular case) yaw is accompanied by roll in the direction of yaw. If the aeroplane is neutrally stable in roll, then a sideslip in the direction of yaw will follow, ending up in a spiral dive: the aeroplane constantly turning into a relative wind caused by perpetual sideslip. If directional stability is weak and the rolling moment is strong, then yaw will be accompanied by a roll away from the direction of yaw, a motion that reduces the sideslip and then reverses it. Resultant motion is an uncomfortable oscillation in roll accompanied by a cyclic yawing, to the pilot it gives the feeling that the aeroplane is slowly wagging its tail from side to side. Dutch roll, as the motion is called, is commonly experienced with aircraft with swept wings. Many such aircraft have grown separate fins beneath the rear fuselage to increase the

directional stability and thus reduce the relative power of the lateral stability. 8.4.1 Dihedral and anhedral

When an aeroplane is viewed from the nose it will be noticed that the wings are set at an angle to the

fuselage. If the wings are inclined upwards, the tips being higher than the roots, they are said to have dihedral. The reverse, with the tip set lower than the root is anhedral. Most low subsonic aircraft have dihedral, while aircraft designed for increasingly higher speeds have less and less dihedral. Many supersonic aeroplanes have anhedral. It is no accident that increasing anhedral is associated with leading-edge sweep and decreasing aspect ratio.

Figure 8.16(a) shows the simplest case of an aeroplane Sideslipping under the influence of a component of weight, W sin φ, where φ is the angle of bank.

Fig. 8.16 Effect of sweepback upon apparent dihedral.

angle of attack than the other. The result is more lift on the leading wing and a rolling moment away from the direction of slip that reduces the bank. Anhedral results in the leading wing having a smaller angle of attack than the wing on the trailing side, and a rolling moment is produced that tends to increase the angle of bank. It should be noted that low-winged aeroplanes have more dihedral (or less anhedral) than the high-winged varieties. The reason being that the CG of a high-winged machine lies below the aerodynamic centre and, rather like a pendulum, the low-set weight tends to hold the wings level. Put another way, the moments of lift and drag of a high-set wing, in acting above the CG, tend to roll the aeroplane upright.

A swept wing, such as is shown in Fig. 8.16(b), experiences a higher velocity normal airflow past the leading wing than past the trailing wing when Sideslipping. The lift of the leading wing is therefore higher than that of the trailing wing, and a strong rolling moment is generated. The greater the sweep or the larger the angle of attack, the more powerful the dihedral effect of a swept wing. For that reason anhedral is used to counter the dihedral effect of sweep. It should be noted, however, that the anhedral on the tailplane in Plate 8-2 is countered by dihedral outboard on the Phantom wing, even though the wings are swept. 8.4.2 The vertical tail

Determination of fin size is not quite such a straightforward problem as might be thought from its apparent simplicity as a surface, because the fin efficiency is affected by an unusually large number of ‘dirty flows’ from the airframe ahead of it. Fin size and dihedral of both wing and tailplane are correlated. Alteration of one invariably affects the efficiency of the others.

Straight-winged propeller-driven aeroplanes have vertical tail areas around 1/2 to 2/3rds of the horizontal tail area. The actual size is determined by the required yawing moment that must be generated when Sideslipping, and this in turn depends upon such important factors as asymmetric engine failure and the EAS. There is the further consideration of rolling moment caused by sideslip in relation to the yawing moment. The total rolling moment should be between 0.75 and 1.0 times the yawing moment caused by the same slip, but the fin contributes in turn to the rolling moment, and so does the wing position on the fuselage. A swept wing makes a favorable contribution to the yawing moment due to sideslip, as may be deduced from Fig. 8.16(b).

A high-set fin causes a lateral rolling moment with sideslip that augments the dihedral effect of the wing. However, as the angle of attack is increased, by a change of airspeed or change of altitude, the fin is borne deeper into the wake shed by the fuselage, so that the effectiveness of the fin is decreased.

Dutch-rolling is most noticeable at height, where the angle of attack is increasing to maintain lift. It is also noticeable during steep climb-outs from airfields in the hotter parts of the world where air density is low. A fin set beneath a fuselage becomes more effective at large angles of attack (and works against dihedral) a fin above the fuselage is less effective.

The modern, clean, high-speed aeroplane requires a much larger fin than a slower aeroplane for the same role. Invariably there is not enough fin and, if the situation cannot be improved by the addition of strakes, then artificial stability (automatic rudder or fin deflection) must be introduced.

A fin surmounted by a high tailplane and terminating in a fuselage at its root is effectively borne between 2 aerodynamic endplates. As such the effective aspect ratio is increased and the fin becomes more powerful as a stabilizer. When the tailplane is set low one of the endplates is removed and the effective aspect ratio of the fin is reduced. Although the side-force generated by a low aspect ratio fin is less for a given angle of yaw than one of higher aspect ratio, there is less proneness to fin-stalling. As fin-stalling is inevitably

catastrophic, fins are usually of lower aspect ratio than any other surface. The larger required area is accepted as a justifiable penalty. In many cases aeroplanes grow dorsal fin extensions during later development. The dorsal extension serves to reduce the fin aspect ratio. As shown in Fig. 8.17, it does not improve the

effectiveness of the fin very much at small angles of sideslip, but it has very powerful anti-stall and stabilizing properties at large angles.

Aerobatic aeroplanes usually have a large portion of the fin surface lying ahead of the tailplane, or a large portion of the fin and rudder lying behind its trailing edge. This arrangement helps to avoid fin and rudder blanketing at large angles of attack during a spin.

Fig. 8.17 Effect of a dorsal fin on yawing moment. Lockheed Blackbird

The Lockheed A-12 was an advanced aeroplane, significantly ahead of its time. It was designed for stealth, exceptionally high performance and long range by the Lockheed 'Skunk Works’, under Clarence L. ‘Kelly’ Johnson. Proposed in 1959, it derived from the earlier A-11, intended to reach M = 3.2 and an altitude at the end of its cruise of 97,600 ft, with a maximum range of 4,120nm (3,800nm at altitude). The A-11 incorporated unusual features: a long gooseneck forward fuselage, a rear-set delta wing, twin engines with reheat and spiked centre-bodies, and twin inward-canted fins and rudders. Quietly, in due course the A-11 was redesignated the A-12 by the company.

(picture)

Plate 8.3 Lockheed SR-71B, two-seater, designed in the ‘Skunk Works’ for stealthy reconnaissance at high altitude. This one, with two pilot stations, is now used for high-speed, high-altitude research into

aerodynamics, propulsion, structures, thermal protection, materials and instrumentation. It is part of a program which, one expects, aims at a future supersonic transport program, in addition to supersonics and hypersonics (see also Appendix E).

Fig. 8.18 The Lockheed ‘Skunk Works’ triple-sonic, long-range, high-altitude interceptor, YF-12, and SR-71, for stealthy reconnaissance. Both are mid-1960s developments of the Lockheed A-11/A-12 and are valuable research tools.

The A-12 revealed such potential, that in 1959 the airframe and powerplant combination was used as the basis for the YF-12 Blackbird, a two-seat, high-altitude, all-weather interceptor, able to reach M = 3.35, with a service ceiling of 85,000ft. In turn, a post-strike reconnaissance aeroplane, the SR-71 Blackbird, was

developed, aimed at becoming operational in 1967. This aeroplane had sharp chines running forward to the nose, in place of the radome (Fig. 8.18).

The family of aeroplanes shared substantially the same configuration, marked by slender, lifting forebody and nacelles with sharp-edged lateral strakes running down their sides. Their twin fins and rudders were mounted on the engine nacelles, with an additional folding fin beneath the rear fuselage. Although the fins were canted inwards to scatter radar returns, it was found that they were affected favorably by the powerful vortices shed by the chines, such that the directional stability improved with increasing angle of attack. They also reduced the rolling moment with yaw (dihedral-effect), which if too powerful causes ‘Dutch-roll’.

Essentially tailless, nevertheless the chinned forebody acted like a foreplane, providing substantial lift by being set at a larger angle of incidence than the wings. This gave the wing the appearance of wash-out relative to the forebody. In fact together they were arranged so as to provide a longitudinal ‘vee’ between them: the surface ahead of the CG being set at a larger angle than that behind.

The ‘vee’ between the planes is a common aerodynamic feature in all aeroplane design with

conventional manual controls, which need a real trim point for the pilot (see Figures 8.12 and 8.13). Usually it can be clearly seen in the geometry of a layout. Sometimes it is less apparent, because although the

longitudinal 'vee’ is there aerodynamically, if the downwash behind a wing is particularly powerful, the

tail-setting angle may be such that the geometric longitudinal dihedral can appear reversed. In the case of the Blackbird family, with powered controls and artificial stability, the apparent ‘vee’ appears to provide the lower aspect ratio forebody with more angle of attack than the wings, which have a higher aspect ratio, to optimize longitudinal lift distribution for maximum supersonic lift/drag ratio.