oscillation in a roll. The Dutch-roll period is short – on the order of a few seconds.

In other words, the main contributors to the Dutch roll are two forms of static stability: the directional stability provided by the V-tail and the lateral stability provided by the effective dihedral and sweep of the wings – both forms offer damping. In response to an initial disturbance in a roll or yaw, the motion consists of a combined lateral–directional oscillation. The rolling and yawing frequencies are equal but slightly out of phase, with the roll motion leading the yawing motion.

Snaking is a pilot term for a Dutch roll, used particularly at approach and landing when a pilot has difficulty aligning with the runway using the rudder and ailerons. Automatic control using yaw dampers is useful in avoiding the snaking/Dutch roll. Today, all modern transport aircraft have some form of yaw damper. The FBW control architecture serves the purpose well.

All aircraft experience the Dutch-roll mode when the ratio of static directional stability and dihedral effect (i.e., roll stability) lies between the limiting conditions for spiral and directional divergences. A Dutch roll is acceptable as long as the damping is high; otherwise, it becomes undesirable. The characteristics of a Dutch roll and the slow spiral are both determined by the effects of directional and lateral stability; a compromise is usually required. Because the slow-spiral mode can be controlled relatively easily, slow-spiral stability is typically sacrificed to obtain satisfactory Dutch-roll characteristics.

High directional stability (Cnβ ) tends to stabilize the Dutch-roll mode but reduces the stability of the slow-spiral mode. Conversely, a large, effective dihedral (rolling moment due to sideslip, Clβ ) stabilizes the spiral mode but destabilizes the Dutch-roll motion. Because sweep produces an effective dihedral and because low-wing aircraft often have excessive dihedral to improve ground clearance, Dutch-roll motions often are poorly damped on swept-wing aircraft.

4.Roll Subsidence. The fourth lateral mode is also nonoscillatory. A pilot commands the roll rate by application of the aileron. Deflection of the ailerons generates a rolling moment, but the aircraft has a roll inertia and the roll rate builds up. Very quickly, a steady roll rate is achieved when the rolling moment generated by the ailerons is balanced by an equal and opposite moment proportional to the roll rate. When a pilot has achieved the desired bank angle, the ailerons are neutralized and the resisting rolling moment very rapidly damps out the roll rate. The damping effect of the wings is called roll subsidence.

12.7 Spinning

Spinning of an aircraft is a post-stall phenomenon (see [5]). An aircraft stall occurs in the longitudinal plane. Unavoidable manufacturing asymmetry in geometry and/or asymmetric load application makes one wing stall before the other. This creates a rolling moment and causes an aircraft to spin around the vertical axis, following a helical trajectory while losing height – even though the elevator has maintained in an up position. The vertical velocity is relatively high (i.e., descent speed on the order of 30 to 60 m/sec), which maintains adequate rudder authority, whereas the wings have stalled, losing aileron authority. Therefore, recovery from a spin is by

the use of the rudder, provided it is not shielded by the H-tail (see Section 4.9). After straightening the aircraft with the rudder, the elevator authority is required to bring the aircraft nose down in order to gain speed and exit the stall.

Spinning is different than spiraling; it occurs in a helical path and not in a spiral. In a spiral motion, there is a large bank angle; in spinning, there is only a small bank angle. In a spiral, the aircraft velocity is sufficiently high and recovery is primarily achieved by using opposite ailerons. Spin recovery is achieved using the rudder and then the elevator.

There are two types of spin: a steep and a flat-pitch attitude of an aircraft. The type of spin depends on the aircraft inertia distribution. Most general-aviation aircraft have a steep spin with the aircraft nose pointing down at a higher speed, making recovery easy – in fact, the best aircraft recover on their own when the controls are released (i.e., hands off). Conversely, the rudder authority in a flat spin may be low. A military aircraft with a wider inertia distribution can enter into a flat spin from which recovery is difficult and, in some cases, impossible. A flat spin for transport aircraft is unacceptable. Records show that the loss of aircraft in a flat spin is primarily from not having sufficient empennage authority in the post-stall wake of the wing.

The prediction of aircraft-spinning characteristics is still not accurate. Although theories can establish the governing equations, theoretical calculations are not necessarily reliable because too many variables are involved that require accurate values not easily obtainable. Spin tunnels are used to predict spin characteristics, but the proper modeling on a small scale raises questions about its accuracy. In particular, the initiation of the spin (i.e., the throwing technique of the model into the tunnel) is a questionable art subjected to different techniques. On many occasions, spin-tunnel predictions did not agree with flight tests; there are only a few spin tunnels in the world.

The best method to evaluate aircraft spinning is in the flight test. This is a relatively dangerous task for which adequate safety measures are required. One safe method is to drop a large “dummy” model from a flying “mother” aircraft. The model has onboard, real-time instrumentation with remote-control activation. This is an expensive method. Another method is to use a drag chute as a safety measure during the flight test of the piloted aircraft. Spin tests are initiated at a high altitude; if a test pilot finds it difficult to recover, the drag chute is deployed to pull the aircraft out of a spin. The parachute is then jettisoned to resume flying. If a test pilot is under a high g-strain, the drag chute can be deployed by ground command, where the ground crew maintains real-time monitoring of the aircraft during the test. Some types of military aircraft may not recover from a spin once it has been established. If a pilot does not take corrective measures in the incipient stage, then ejection is the routine procedure. FBW technology avoids entering spins because air data recognize the incipient stage and automatic-recovery measures take place.

12.8 Design Considerations for Stability: Civil Aircraft

From the discussion on aircraft behavior in a small disturbance, it is clear that both aircraft geometry and mass distribution are important in the design of an aircraft with satisfactory flying qualities. The position of the CG is obtained by arranging the

aircraft components relative to one another to suit good in-flight static stability and on-ground stability for all operational envelopes. The full aircraft and its component moments are estimated semi-empirically (e.g., DATCOM and RAE data sheets) as soon as drawings are available and followed through during the next phase; the prediction is improved through wind-tunnel tests and CFD analyses. In the conceptual design stage, the control area on the wing and empennage (i.e., flap, aileron, rudder, and elevator) are sized empirically from past experience (and DATCOM and RAE data sheets). However, the CG position relative to the aircraft NP is tuned afterwards.

Chapter 6 describes the aerodynamic design of major aircraft components. Chapter 11 considers the sizing of the wing and empennage and also establishes the matched-engine size. Whereas statistics of past designs proved vital for configuring the empennage, the placement of components relative to one another is based on a designer’s experience, which forms a starting point for the conceptual design phase.

The important points affecting aircraft configuration are reviewed as follows:

1.Fuselage. The fuselage has a destabilizing effect – the fuselage lift (although minimal) and moment add to instability – and its minimization is preferred. In addition to keeping costs down, the fuselage may be kept straight (with the least camber). Mass distribution should keep inertia close to the fuselage centerline. A BWB requires special considerations.

The fuselage length and width are determined from the payload specifications. The length-to-average-diameter ratio for the baseline aircraft version may be around 10. The closure angles are important, especially the gradual closure of the aft end, which should not have an upsweep of more than what is necessary – even for a rear-loading door arrangement that must have an upsweep. The front closure is blunter and must provide adequate vision polar without excessive upper-profile curvature.

For a pressurized cabin, the cross-section should be maintained close to the circular shape. Vertical elongation of the cross-section should be at a minimum to accommodate the below-floorspace requirements. For small aircraft, fuselage-depth elongation may be due to placement of the wing box; for larger aircraft, it may be due to the container size. Care must be taken so that the wing box does not interfere with the interior cabin space. Generous fairing at the wing–body junction and for the fuselage-mounted undercarriage bulge is recommended. An unpressurized fuselage may have straight sides (i.e., a rectangular cross-section) to reduce the production costs. In general, a rectangular fuselage cross-section is used in conjunction with a high wing. The undercarriage for a high-wing aircraft has a fuselage bulge.

2.Wing. Typically, an isolated wing has a destabilizing effect unless it has a reflex at the trailing edge (i.e., the tail is integrated into the wing such as all-wing aircraft like the delta wing and BWB). The larger the wing camber, the more significant is the destabilizing effect. Optimizing an aerofoil with a high L/D ratio and with the least Cm wing is a difficult task not discussed herein. Wind-tunnel tests and CFD analyses are the ways to compromise. It is assumed that aerodynamicists have found a suitable aerofoil with the least destabilizing moment for

Equation 12.2 provides insight to the pitching-moment contribution from the geometrical arrangement. It shows that minimizing the vertical distance of the components from the aircraft CG also minimizes their pitching-moment contributions.

5.Empennage. The empennage configuration is of primary importance in an aircraft design. The reference sizes are established by using statistical values of tailvolume coefficients, but the positioning and shaping of the empennage require considerable study. This is another opportunity to check whether the statistical values are adequate. The sweeping of the empennage increases the tail arm and may also enhance the appearance; even low-speed, smaller aircraft incorporate sweep. Chart 4.2 and Figures 4.24 and 4.25 show several possible empennage configurations.

A conventional aircraft H-tail has a negative camber, the extent depending on the moment produced by an aircraft’s tail-less configuration, as described previously. For larger, wing-mounted turbofan aircraft, the best position is a low H-tail mounted on the fuselage, the robust structure of which can accommodate the tail load. A T-tail on a swept V-tail increases the tail arm but should be avoided unless it is essential, such as when dictated by an aft-fuselage–mounted engine. T-tail drag is destabilizing and requires a larger area if it is in the wing wake at nearly stalled attitudes. The V-tail requires a heavier structure to support the T-tail load. Smaller turbofan aircraft are constrained with aft-fuselage- mounted engines, which force the H-tail to be raised up from the middle to the top of the V-tail. The canard configuration affords more choices for the aircraft CG location. In general, if an aircraft has all three surfaces (i.e., canard, wing, and H-tail), then they can provide lift with a positive camber of their sectional characteristics. It is feasible that future civil aircraft designs of all sizes may feature a canard.

Typically, a V-tail has a symmetric aerofoil but for propeller-driven airplanes, it may be offset by 1 or 2 deg to counter the skewed flow around the fuselage (as well as gyroscopic torque).

The discussion is the basis for the design of any other type of empennage configuration, as outlined in Table 4.2. If a designer chooses a twin-boom fuselage, the empennage design must address the structural considerations of twin booms. (Tail-less aircraft are less maneuverable.)

An H-tail also can be dihedral or adhedral, not necessarily for stability reasons but rather to facilitate positional clearances, such as to avoid jet efflux.

6.Undercarriage. A retracted undercarriage does not contribute to the aerodynamic load but when it is extended, it generates substantial drag, creating a nose-down moment. To address this situation, there should be sufficient elevator nose-up authority at a near-stall, touch-down attitude, which is most critical at the forwardmost CG position. Designers must ensure that there is adequate trim authority (i.e., the trim should not run out) in this condition.

7.Use of Any Other Surface. It is clear how stability considerations affect aircraft configurations. Despite careful design, an aircraft prototype may show unsatisfactory flying qualities when it is flight-tested. Then, additional surfaces (e.g., ventral fin and delta fin) may be added to alleviate the problem. Figure 12.15 shows two examples of these modifications. It is preferable to avoid the need for additional surfaces, which add penalties in both weight and drag.