Computed Tomography Data

The longitudinal and lateral controls are combined into elevons, which operate together for pitch control and differentially for roll control. To realise the advantages of a differential aileron system, a two control surface combination is required, as illustrated in Fig. 2.17.

Nickel and Wohlfart (1994) explain that the outer surfaces work differentially as ailerons, whilst the inner surfaces not only support the aileron effect, but also take care of the balance of pitching moments about the lateral axis. For the example here, the inner surface on the left is more deflected than the outer surface on the right because it has to balance the pitching moments at a shorter lever arm due to the sweep back.

Figure 2.17: Differential elevon control for a pure aileron deflection to the right without any elevator effect (from Nickel and Wohlfart (1994)).

Trim control is achieved on tailless aircraft with the aid of elevator control surfaces located

2.2. THE FLYING WING CONFIGURATION

at the trailing edge of the wing. To produce the same change inCm, the elevator of a tailless aircraft must be deflected more than that of a conventional aircraft of the same static margin.

With aircraft generally having an overall nose-down pitching moment, upward deflection of these surfaces generates down-lift over the trailing edge, increasing the profile moment of the wing section. This not only reduces the local section C_l but also C_L,max, worsening as the static margin increases (Nickel and Wohlfart (1994)). However, Northrop (1957) comments that the required elevator trim will be less for tailless aircraft with close to neutral static stability.

Northrop (1957) chose to eliminate vertical fin and rudder control surfaces, firstly because they violate the all-wing principle and add drag to the basic aerofoil; whilst secondly, for designs incorporating a moderate amount of sweepback, the moment arm of a conventional rudder about the CG is small and an excessively large rudder would result when aiming to achieve conventional yaw control moments. However, Nickel and Wohlfart (1994) comment that wingtip fins are not only useful for steering but also increase directional stability, whilst decreasing induced drag. Nevertheless, Northrop (1957) concentrated on trying to find a type of drag-producing device at the wing tips that would give adequate yawing forces, without affecting pitch or roll. The drag needed is not very large since it works over quite a long lever arm, about half-span.

A double-split flap at the wing tip was found to have the most satisfactory all-round char-acteristics, whilst allowing for the combination of a trim flap and rudder in the same portion of wing trailing edge; however, it does suffer from low effectiveness at low angles of rudder deflection, and in addition Nickel and Wohlfart (1994) comment that besides increased con-struction complexities, the departing vortices associated with double-split flaps often induce vibrations on the flaps. Nevertheless, the double-split flap was adopted by Northrop on the B-2 bomber, as illustrated in Fig. 2.18. ¹.

Spin recovery is generally accomplished by deflecting the ailerons such that a rolling moment is generated to counter the spin. However, Donlan (1944) explains that wingtip fins are also effective for spin recovery, especially if the rudder extends below the wing in order to overcome/reduce the blanketing effects of the wing. In contrast, drag rudders were not found to be very successful due to the varying nature of performance of those located in stalled and unstalled regions — in some cases they were even found to produce pro-spin rolling moments.

Rudder control is not only necessary to counter the effects of adverse yaw, but also to trim the aircraft directionally under asymmetric power conditions. Donlan (1944) proposes that, to reduce the rudder control requirements, the thrust lines should be located as close as

1http://upload.wikimedia.org/wikipedia/commons/thumb/b/be/USAF 2 Spirit.jpg/600px-USAF B-2 Spirit.jpg

Figure 2.18: B-2 split flap rudders.

possible to the centreline and ailerons that create favourable yawing moments when deflected should be adopted. Bolsunovsky et al. (2001) also suggest the use of split flap elevons in addition to vertical rudder control surfaces in order to provide extra yaw control.

2.2.3.4 Effects of Wing and Planform Geometry on Stability and Control Sweep

Figure 2.19 shows that sweeping the wing significantly changes the lift distribution. A ‘lift valley’ results toward the centreline, whilst a ‘lift mountain’ develops toward the wing tips, becoming more pronounced as the angle of sweepback increases. (Sweeping the wings forward has the opposite effect; however, this is not practical from the perspective of attaining lon-gitudinal static stability on (Donlan (1944), Northrop (1957), Nickel and Wohlfart (1994)).) For an unswept wing of normal aspect ratio, the NP is located at around quarter-chord.

However, as the aspect ratio is reduced to very low values, Jones (1941) states that the NP moves ahead and upward, making the attainment of stability and balance more difficult.

With the majority of the payload accommodated toward the centreline of the aircraft, an increase in positive static margin will result with increased sweepback, producing favourable conditions for longitudinal static stability (Nickel and Wohlfart (1994)). The increased effec-tive lever arm gives good trim characteristics; however, although the moment produced for

2.2. THE FLYING WING CONFIGURATION

Figure 2.19: The lift distributions of two rectangular wings with an aspect ratio of 5 and sweep angles of φ= 0^◦ andφ= 45^◦. The lift distribution of the swept wing has been plotted for equal lift (solid line) and for the same angle of attack (dashed line). (Taken from Nickel and Wohlfart (1994)).

a given control surface deflection increases with sweep, the overall response of the aircraft is also affected by the increased moment of inertia about the lateral axis. Sweep also con-tributes to the effectiveness of wingtip fins (see below), producing more directional stability and rudder control or, alternatively, allowing them to be made smaller. There is the possi-bility of using centre spanwise surfaces as high-lift devices, whereby lift increments produce only minor changes in pitching moment. Jones (1941) explains that sweepback increases the effective dihedral, and that this effect is strongly dependent on angle of attack (increasing with lift coefficient). He adds that the lateral stability and control characteristics of tailless aircraft should be able to approach those of conventional aircraft, and concludes that weath-ercock stability can be secured provided sweepback is combined with either negative dihedral or wingtip fins. Sweepback helps prevent the occurrence of α-oscillations (also known as pecking) — an oscillatory motion about the lateral axis — which can become problematic in gusty weather conditions (Donlan (1944)). Although tumbling has been shown not to be particularly troublesome, an increased amount of sweep helps prevent its occurrence (Nickel and Wohlfart (1994)).

Swept-back wings have an inherent tendency to undergo premature tip stall, especially during high-lift flight conditions such as take-off and landing. This is a very serious condition, as the aircraft will tend to “roll-off” around the longitudinal axis, and as it is a self-amplifying process (Nickel and Wohlfart (1994)). Tip stall also has an increased tendency to arise when the aircraft is yawing. Donlan (1944) shows that it first occurs over the rear portion of the

wing where the control surfaces are located; hence, it is likely that aileron control will be ineffective. Furthermore, the tip stall also manifests as a pitching instability, as the loss of lift often occurs behind the CG. Ground clearance issues may therefore become of importance, necessitating dihedral (though this in turn increases the skid-roll moment). Finally, flying wings with large sweepback have a stronger tendency to Dutch roll.

Taper

Taper is the other main parameter which influences both the aerodynamic performance of the FW and its construction. One specific advantage of taper is that the volume of material decreases outboard, with the largest amount of usable spar height in the wing centre (where the highest spar bending moments occur). Therefore the spar can be built smaller overall, resulting in a reduction in aircraft weight. In addition, there is a reduction in the intensity of the span loading moving outboards. Thus the outer spar sections can be built lighter, which means a concentration of weight closer to the centreline, which in combination with sweep favours a positive static margin and increased directional stability. Strong tapering does however increase the danger of wingtip stall with higher local values ofCl outboard.

Aerofoil Section

On tailless aircraft, a nose-down aerofoil pitching moment cannot be compensated for by a horizontal stabiliser, therefore the aerofoil section CM0 is important. Although sweep and washout can be used to an extent for balance, alone they are unable to counter very large pitching moments. Therefore, tailless aircraft having small, or even zero, zero-lift pitching moments are preferable. This may be obtained either with a symmetrical aerofoil or a reflexed aerofoil, whereby a convex leading edge generates most of the lift whilst the concave rear part provides stability. A disadvantage with symmetric sections is that they have their minimum drag at zero lift, therefore a lifting wing would have more drag than could be achieved with a properly cambered wing to match the cruise lift coefficient.

In general, the aerofoil section only has a slight affect on the NP (Nickel and Wohlfart (1994)). However, Jones (1941) notes that an extreme reduction in thickness toward the trailing edge can slightly shift the NP rearwards.

Washout

The required washout distribution depends on the lift coefficient at which the aircraft flies with neutral elevators. Nickel and Wohlfart (1994) explain that with a low degree of washout, the elevators are neutral at high speed but are permanently deflected at low speeds. The

2.2. THE FLYING WING CONFIGURATION

opposite is true for a large degree of washout. The latter condition is less desirable as there is a drag penalty over a much longer flight time. For a fixed designC_L, static margin and low CM0, the required amount of washout increases with a drop in planform sweep and aspect ratio. Washout may be used to mitigate the effects of wingtip stall by reducing local C_l, but at the cost of a reduced overall C_L. Nickel and Wohlfart (1994) add that the NP position is also independent of washout.

Wingtip Fins

Nickel and Wohlfart (1994) explain that the overall influence of wingtip fins on the local lift density is a reduction over the wing centre, and an increase towards the tips of the basic wing. This effect: shifts the neutral point of a sweptback wing further aft, increasing the longitudinal static margin; improves aileron effectiveness; and contributes to a reduction in induced drag below the ‘optimum’ elliptic case for a plane wing — also noted by Lee (1961);

gives the wing an effective dihedral by generating a skid-roll moment; finally, helps reduce, even eliminate, unwanted adverse yaw effects, due to the strong vortex generated by an aileron deflection which combines with the wingtip fin to produce an opposing side force.

As the lift density is approximately equal on both sides of the wing bend, Nickel and Wohlfart (1994) suggest that it is appropriate to give the wingtip fins the exact same aerofoil shape installed at the tips of the basic wing. However, there does not seem to be an optimum wingtip fin planform, i.e. sweep, taper and aspect ratio.