Category Airplane Stability and Control, Second Edition

While scientists and mathematicians in the United States and Europe built the foundations of future advances by developing fundamental aeronautical theory, practical aeronautical designers invented and improved the airplane empirically. As recognized by the Wright brothers, solutions to the stability and control problem had to be found. This chapter presents the largely empirical development of airplane stability and control from the precursors of the Wrights through the end of the first World War. It was only then that aeronautical theory started to have an impact on practical airplane design.

1.1 Inherent Stability and the Early Machines

Pioneer airplane and glider builders who came before the Wright brothers recog­nized the importance of airplane stability. They had discovered that some degree of inherent stability in flight could be obtained with an appropriate combination of aft-mounted tail surfaces (Cayley and Penaud), wing dihedral angle or lateral area distribution (Langley and Lanchester), and center of gravity location (Lilienthal).

However, very little thought had been given to the problem of control except for the provision of horizontal and vertical rudders (Langley et al.). It was commonly held that an airplane should hold its course in the air while the pilot decided what to do next. Then the pilot would deflect the rudder to steer it, more or less in the manner of a boat. Only the Wrights recognized that (1) an airplane has to be banked to turn in a horizontal plane; (2) an interaction exists between the banking or roll control and the yawing motion of an airplane; (3) excessive dihedral effects hinder pilot control unless sideslip is suppressed and makes the machine unduly sensitive to atmospheric turbulence; (4) wings can be stalled, leading to loss in control; and (5) control can be regained after stalling by reducing the angle of attack.

After the Wright brothers, Bleriot and Levavasseur, the constructor and designer of the Bleriot and Antoinette machines, respectively, pioneered in developing tractor monoplanes with normal tail surfaces and wing dihedral angles (Figure 1.1). These two airplanes had a fair amount of inherent stability, unlike the Wright biplanes. They had superior speed, which helped establish the aft tail as the normal arrangement. In fact, the Bleriot and Antoinette machines were the transitional forms that led from the Wright brothers’ biplanes to the famous pursuit airplanes of World War I.

A remarkable paper by a Cal Tech professor was a source for years afterwards of propeller power effects on static longitudinal and directional stability (Millikan, 1940). Millikan’s paper was based primarily on test results from Cal Tech’s Guggenheim Aeronau­tical Laboratories’ (GALCIT) low-speed wind tunnel. The tunnel staff and the companies who tested new aircraft models there had the foresight to develop both the hardware and techniques needed to run tests that simulated power-on flight conditions. The primary hard­ware need was for compact, powerful electric motors that could be mounted inside model fuselages(Figure 4.1). Electric motorsof thistype with larger diametersand lower power had been designed and installed in British N. PL. wind tunnel models much earlier (Relf, 1922).

Testing techniques required that model thrust be adjusted to predicted full-scale condi­tions. This ensured that the slipstream velocities behind the model propellers were in the correct proportions to free-stream velocities. Propeller effects on stability and control arise from two other factors aside from the slipstreams washing over wings, tail surfaces, and fuselages. These are the simple direct-thrust moments in pitch and yaw and the forces and moments acting on the propellers themselves. The following sections trace the development of our understanding of these effects.

In fly-by-wire systems control surface servos are driven by electrical inputs from the pilot’s controls. Single-channel fly-by-wire has been in use for many years, generally through airplane automatic pilots. For example, both the Sperry A-12 and the Honeywell

C-1 autopilots of the 1940s provided pilot flight control inputs through cockpit console controls. However, in modern usage, fly-by-wire is defined by multiple redundant channel electrical input systems and multiple control surface servos, usually with no or very limited mechanical (cable) backup.

According to Professor Bernard Etkin, a very early application of fly-by-wire technology was to the Avro Canada CF-105 Arrow, a supersonic delta-winged interceptor that first flew in 1958. A rudimentary fly-by-wire system, with a side-stick controller, was flown in 1954 in a NASA-modified Grumman F9F (Chambers, 2000). The NASA/Dryden digital fly-by­wire F-8 program was another early development. Readers can consult Schmitt (1988) and Tomayko (2000) for the interesting history of airplane fly-by-wire.

The Boeing 767 is probably the last design from that company to retain pilot mechanical inputs to irreversible power control actuators, or fly-by-cable. The 767 elevator control schematic shows a high redundancy level, with three independent actuators on each elevator, each supplied by a different hydraulic system (Figure 5.17). Automatic pilot inputs to the system require separate actuators, since the primary surface servos do not accept electrical signals.

The Boeing 777 is that company’s first fly-by-wire (FBW) airplane, in which the primary surface servos accept electrical inputs from the pilot’s controls. With the Boeing 777, fly­by-wire can be said to have come of age in having been adopted by the very conservative Boeing Company. Fly-by-wire had previously been operational on the Airbus A320, 330, and A340 airplanes

Figure 5.18 (Osder 1999) shows the redundancy level provided on the Boeing 777 control actuators. In this figure PFC refers to primary flight control computers, the ACE are actuator control electronic units, the AFDC are autopilot flight director Controls, the PSA are power

supplies, and the FSEU are secondary control units. Note the cross-linkages of the ACEs to the hydraulic power sources.

McLean (1999) gives interesting details on the 777 and A320 fly-by-wire systems:

[Boeing 777] …to prevent pilots exceeding bank angle boundaries, the roll force on the column increases as the bank angle nears 35 degrees. FBW enables more complex inter-axis coupling than the traditional rudder crossfeed for roll/yaw coordination which results in negligible sideslip even in extreme maneuvers… the yaw gust damper (which is independent and separate from the standard yaw damper on the aircraft)… senses any lateral gust and immediately applies rudder to alleviate loads on the vertical fin. The Boeing 777 has an FBW system which allows the longitudinal static margin to be relaxed – a 6 percent static margin is maintained… stall protection is provided by increasing column control forces gradually with increases in angle of attack. Pilots cannot trim out these forces as the aircraft nears stall speed or the angle of attack limit.

[Airbus 320].. . sidestick controllers are used. The pitch control law on that aircraft is basically a flight path rate command/flight path angle hold system and there is exten­sive provision of flight envelope protection… the bank angle is limited to 35 degrees

There is pitch coordination in turns. A speed control system maintains either VREF [a reference airspeed] or the speed which is obtained at engagement. There is no mechanical

backup___ Equipment has to be triplicated, or in some cases quadruplicated with automatic

“majority voters” and there is some provision for system reconfiguration.

The two cases illustrate an interesting difference in transport fly-by-wire design philoso­phy. Boeing 777 pilots are not restricted from applying load factors above the limit, except by a large increase in control forces. Wings could be bent in an emergency pullout. Airbus control logic prevents load factors beyond limit.

The McDonnell Douglas F/A-18 Hornet represents a move in the direction of completely integrated flight control actuators. Pilot inputs to the F/A-18’s all-moving horizontal tail or stabilator are made through two sets of dual solenoid-controlled valves, a true “fly-by-wire”

.MECHANICAL FEEDBACK UVPICAO
SERVOVALVE ISVIL	SERVOVALVE ISV? I
CENTERING SPRING
I SERVOVALVE <3 (SV3>
FAILSAFE SOIENOIO VALVE IDE-ENtRGlZEOl
(PRESSURE T#F TO CLOSE SWITCHI

INLET CHECK

RESTRICTOR

Figure 5.19 Photograph and schematic of the General Dynamics F-16 Integrated Servo Actuator (ISA) made by the National Waterlift Company. This actuator design is typical of an entirely fly-by­wire flight control system. The actuator uses mechanical rate (main valve spool position) and position feedback, although electrical feedback has been tried. Internal hydromechanical failure detection and correction, using three independent servovalves, causes the piping complexity. (Reprinted with per­mission from SAE Paper No. 831483, @ 1983, Society of Automotive Engineers, Inc.)

system. A mechanical input from the pilot is applied only in the event of a series of electrical failures and one hydraulic system failure.

The General Dynamics F-16 is a completely fly-by-wire airplane, incorporating fully integrated servoactuators, known by their initials as ISAs. Each actuator is driven by three electrically controlled servo valves (Figure 5.19). There are no mechanical valve inputs at all from the pilot. Of course, the servo valves also accept signals from a digital flight control computer. The complexity seen in the ISA schematic is due to the failure detection and correction provisions. Only two of the three servo valves operate normally. A first failure of one of these valves shifts control automatically to the third servo valve. A first failure of the third servo valve locks the actuator on the sum of the first two.

The F-16 servoactuators also are used as primary surface actuators on the Grumman X – 29A research airplane. Integrated servoactuators of equivalent technology were developed by Moog, Inc., for the Israeli Lavi fighter airplane.

The Northrop/Lear/Moog design for the B-2 Stealth bomber’s flight controls represents another interesting fly-by-wire variant. On this quite large airplane part of the servo control electronics that normally resides in centralized flight control computers has been distributed close to the control surfaces. Digital flight control surface commands are sent by data bus to actuator remote terminals, which are located close to the control surfaces. The terminals contain digital processors for redundancy management and analog loop closure and compensation circuits for the actuators. Distributing the flight control servo actuator feedback functions in this manner saves a great deal of weight, as compared with using centralized flight control computers for this function (Schaefer, Inderhees, and Moynes, 1991).

Other modern fly-by-wire airplanesinclude the McDonnell DouglasC-17, the Lockheed- Martin F-117 and F-22, the NASA/Rockwell Space Shuttle orbiter, the Antonov An-124, the EF 2000 Eurofighter, the MRCA/Tornado, the Dassault Breguet Mirage 2000 and Rafale, the Saab JAS-39, and the Bell Boeing V-22.

Spin researchers recognized quite early the problems in forming engineering gen­eralities for spinning airplanes. During all spin phases – the entry, the developed spin, and the recovery – airplanes operate in nonlinear ranges of angle of attack, control surface angle, and angular velocities, not to mention inertial moments. Nonlinear behavior means that general­izations require a large body of data obtained by systematic variations in design parameters.

Not long after the NACA 20-foot spin tunnel was put into operation, the veteran spin investigators Oscar Seidman and Anshal I. Neihouse began that process of systematic spin data collection. In a series of NACA Technical Notes and a technical report dating from 1937 to 1948, they reported on the effects of systematic wing, tail, relative density, and mass distribution changes on spin characteristics and recoveries.

With the coming of jet – and rocket-powered airplaneshaving long, slender, heavily loaded fuselages this group, now augmented by Walter J. Klinar and Stanley H. Scher, again picked up the problem of generalizing on spin characteristics by making systematic variations in design parameters. In the new series, the effects of mass distribution were again reviewed, but also the complex aerodynamics of long noses, strakes, and canards (Neihouse, Klinar, and Scher, 1960).

The successful, routine use of wings swept back 30 to 45 degrees is a source of wonder to stability and control engineers who were active in the 1940s. Then, a wing that was tapered by sweeping back the leading edge, while keeping a straight or slightly swept trailing edge, giving no more than about 5 degrees of sweepback, was deplored. One could expect early wing tip stall with increasing angle of attack, wing drop, and roll damping reversal. Airplanes with sweptback leading edges and straight or nearly straight trailing edges included the Douglas DC-3 and the North American SNJ Texan.

11.7.1 Wing Leading-Edge Devices

When really large amounts of wing sweepback became a necessity for high Mach number airplanes, sweptback wings had to be designed that would have decent low-speed stalling chacteristics. It was soon found that large amounts of wing sweepback combined with moderate aspect ratios could be made practical by wing leading-edge devices such as slots, slats, leading-edge flaps, cambers, and blunt-nose radii (Figure 11.10). Fixed-wing leading-edge slots were used before the advent of sweptback wings, to correct wing tip stall on heavily tapered straight wings, such as the Lockheed PV-1 Ventura. But fixed slots obviously added to drag in normal flight. The modern slat or leading-edge flap extends at low airspeeds but retracts fully for cruising flight. When opened, the leading-edge slat or flap delays separation by increasing the local camber.

High suction pressure on the slat’s upper surface as the wing nears the stall was used successfully to open wing slats on the North American F-86 and the Douglas A3D and A4D airplanes, avoiding hydraulic opening and closing systems. These self-opening slats could prove nerve-racking to pilots. When angle of attack is increased one wing slat tends to bang open a bit earlier than the other. However, at the angles of attack considerably below the wing stall point where air loads open the slats the opened slats have little effect on wing lift. While unsymmetrical slats look dangerous, at angles of attack well below the stall the airplane has little or no tendency to roll.

With the coming of better hydraulic systems wing slats are now universally powered. Wing slats are undesirable in some applications, as in stealth airplanes, because of the special treatments needed to avoid radar returns from the slat-wing seams. Where slats are impracti­cal designers have learned to use wing camber and nose radius changes as substitutes. How­ever, it may be doubted whether these measures can be effective as slats in preventing early wing tip stall. Other wing devices to improve stalling characteristics are considered next.

As mentioned in Chapter 5, Sec. 24, analytical redundancy for fly-by-wire control system safety will become feasible only when vehicle system identification operates well under all flight conditions, and not just where linearized, small perturbation equations of motion apply. For this reason, and to generate practical design information, there has been an effort to extend identification to nonlinear and unsteady aerodynamic regimes. The extended Kalman filter mentioned in the previous section can generate full nonlinear aerodynamic models, such as Cm (a,8,q,…), and not just aerodynamic stability derivatives at various operating points.

The transfer function model for unsteady flow (Chapter 10, Sec. 6.1) has been used successfully at the DLR to model lift hysteresis at the stall for the Fairchild/Dornier Do 328 transport. The procedure (Fischenberg, 1999) is in several parts, starting with a steady-state approximation for the point of trailing-edge flow separation at high angles of attack, using static wind-tunnel data. Time dependency is introduced by the assumption that the separation point can be modeled as the solution of a first-order differential equation, equivalent to a single-pole transfer function. A final assumption is that the lift coefficient in trailing-edge separated flow is a function of the separation point, using a model proposed by Kirchoff. Four parameters of the model remain to be identified in flight testing, but when these are found, good comparison of flight measurements of lift coefficent with the modeled values is obtained (Figure 14.18).

The significance of this work is that once the unsteady lift parameters of representa­tive lifting surfaces can be predicted, the basis is in hand for predicting unsteady val­ues of complete airplane stability derivatives. Those derivatives are computed from the forces and moments of the lifting surfaces and the fuselage-type shapes that make up a complete configuration. Future work in this area will presumably deal with leading – edge flow separation models, which are characteristic of thin wings with sharp leading edges, and with predictive models for the unsteady vortex flows that can affect stability derivatives. Stall hysteresis for airfoils with sharp leading edges is discussed by Covert (1993).

In their basic form, the equations of airplane motion are a set of nine simultaneous nonlinear differential equations. One of the most far-reaching steps taken by Bryan was the development of a perturbation, linearized, form of these equations. The perturbation motion of a simple mechanical object, such as a pendulum, about a state of rest is a familiar concept. In his Mecanique Analytique of 1788, J. L. Lagrange developed the theory of small perturbation motions of systems having many degrees of freedom about a position of stable equilibrium. Bryan extended Lagrange’s work by replacing the position of stable equilibrium by a steady equilibrium motion.

The utility of Bryan’s linearization arises from the nature of airplane perturbed motions. Under normal operating conditions, such as personal-airplane and airliner climbs, cruises, and landing approaches, airplanes are among the most linear dynamic systems known. Aerodynamic force and moment are quite closely proportional to airplane perturbed motions, without any equivalent to coulomb friction. Small-perturbation or linearized equa­tions are perfectly suitable to describe the motions experienced by the crew and passengers, and for the design of stability augmenters and automatic pilots.

Bryan analyzed small perturbations about steady, symmetric, rectilinear flight, either level, climbing, or diving. Most of the subsequent literature on airplane dynamics is based on the same model. Equations of perturbed airplane motion about steady turning and steady sideslipping flight came soon after Bryan, in an important 1914 report by Leonard Bairstow. A further extension to general curvilinear flight was made using earth-referred coordinates (Frazer, Duncan, and Collar, 1938). Still later investigators (Abzug, 1954; Billion, 1956) used the more useful body-fixed coordinates. Then, in a series of NASA papers dating from 1981 to 1983, Robert T N. Chen applied linearization to the case of perturbations from uncoordinated turns. Chen’s immediate goal was to represent perturbation motions of single-rotor helicopters in low-airspeed, steep turns, in which appreciable amounts of sideslip are quite normal.

The 1914 linearization work by Bairstow suffered the fate of theory that was too far ahead of its time. The later investigators mentioned above seemed to have been unaware that Bairstow had already extended the original Bryan equations.

Bryan’s linearization of the equations of airplane motion reduces them to two sets of three simultaneous linear differential equations, each set of fourth order. The linearized equations shown in Figure 18.4 illustrate three typical features of these equations. Differentiation is indicated by the Laplace variable s, operating on the small-perturbation quantities such as u, w, в, and в. Aerodynamic variations with small-perturbation quantities, called stability derivatives, are in the “dimensional” form, suitable for closed-loop system studies and for simulation.

Finally, the derivatives are the primed form such as Lp’ rather than Lp for the rolling moment due to rolling velocity. Primed derivatives combine inertial terms with aerody­namic terms, simplifying the lateral set and putting these equations into state-variable form (Sec. 11).

The fact that the linearized equations of motion separate into two independent sets is of enormous significance. Engineers can treat airplane dynamics as two individual problems:

longitudinal stability and control, arising from the symmetric equation set, and lateral stability and control, arising from the asymmetric set. However, separation into independent longitudinal and lateral sets fails for perturbations from curvilinear or sideslipping flight. Coupled lateral-longitudinal equations of up to eighth order result. Bairstow (1920) treated perturbations from circling flight.

While the normal modes are by far the most common way to account for aeroelastic effects on airplane stability and control, the less abstract, approximate normal mode method called quasi-rigid analysis deserves mention. In quasi-rigid analysis, the flexible airplane structure is represented by a chain of linked rigid bodies, held in position by springs. An approximate normal mode is introduced for each link.

The earliest dynamic stability and control analysis in which an airplane bending mode was represented appears to have been the quasi-rigid analysis of the Boeing XB-47 (White, 1947). A single yaw pivot was assumed behind the wing trailing edge. This effectively represents the airplane’s first asymmetric bending mode.

Ground vibration tests had established the B-47’s first bending mode frequency at 2.3 cycles per second. Using the known weight of the airplane’s aft section, the effective spring was sized to produce the measured bending frequency. A closed-loop servo analysis agreed with flight results that showed some vibration at the first bending mode frequency when the yaw damper rate gyro was located near the vertical tail. Moving the gyro near the airplane’s center of gravity corrected the problem.

Just as quasi-rigid analysis has provided a simple, approximate alternative to normal mode analysis, it has done the same for the quasi-static aeroelastic problem. The longitudinal neutral and maneuver points of the Northrop YF-17 were found in this way (Abzug, 1974).

The connection between excessive lead requirements for control and poor pilot ratings is the basis for the Neal-Smith criterion, dating from 1970. A lead-lag pilot model is assumed, with a fixed time delay of 0.3 second. When this pilot model is combined with the dynamics of the airplane, the model parameters can be adjusted to meet bandwidth and other closed-loop requirements. The resultant pilot model phase lead and closed-loop resonance are compared with pilot opinions to establish acceptable boundaries (Figure 21.5).

The Neal-Smith approach is an important contribution to the rationalization of flying qualities requirements since it makes direct use of the mathematical pilot model. The method has shortcomings in that the required pilot lead is strongly dependent on the required bandwidth, an arbitrary starting point (Moorhouse, 1982).

Figure 21.5 Neal-Smith criterion for pitch control. Acceptable short-period behavior occurs below the boundary established by closed-loop peak resonance ratio, the abscissa, and pilot model lead, the ordinate. The hatched boundaries are more restrictive limits proposed for large transports. (From Mooij, AGARD LS-157, 1988)

2.1 Stability and Control Educators

The gap between aeronautical theory and stability and control practice has never entirely closed. However, the number of aeronautical engineers trained in stability and control theory has grown greatly since the subject started to be taught in the aeronautical engineering schools that sprang up starting around 1920.

By 1922, there were already five U. S. universities with programs in aeronautical engi­neering: the Massachusetts Institute of Technology, the California Institute of Technology, the University of Michigan, the University of Washington, and Stanford University. In that same year, Drs. Alexander Klemin and Collins Bliss of New York University offered ele­mentary aerodynamics as an option in mechanical engineering, launching the aeronautical program there. Other U. S. colleges and universities, too numerous to mention, followed in later years. By 1997, the American Institute of Aeronautics and Astronautics (AIAA) had no fewer than 145 student branches in colleges and universities around the world.

Otto C. Koppen was an aviation pioneer who taught airplane stability and control while continuing as a designer of new airplanes. William F. Milliken, Jr. (1947) had this to say about Koppen’s contributions to his own field of airplane dynamics:

Since about 1930 the course of airplane dynamics in this country has been widely and continuously influenced by the research and teachings of Otto C. Koppen. His theoretical investigations, wind tunnel work (oscillators), and achievements in airplane design are now well known. For years his course in stability and control at MIT was unique in its treatments of the complete dynamics, and many current trends in design and research may be traced directly to his work as an educator….

European educators were busy as well. At the time (1911) he wrote Stability in Aviation, G. H. Bryan was a mathematics professor at the University ofNorth Wales. Twenty problems for further research may be found at the end of that book. Airplane stability and control was soon taught widely in Great Britain.

In 1920, the first edition of Leonard Bairstow’s famous book Applied Aerodynamics appeared. That year he was appointed Professor of Aerodynamics at Imperial College. In 1945, Ernest F. Relf and William J. Duncan, both already identified with airplane stability and control, served on a group that established the Cranfield College of Aeronautics, for postgraduate education. Relf became principal, and Duncan became a legendary Cranfield professor.

In Japan, the late Professor Kyuichiro Washizu (1921-1981) played somewhat the same role as did Otto Koppen in the United States. Washizu introduced the concept of airplane stability and control to Japan, at the Department of Aeronautics, the University of Tokyo. His students spread all over Japan, eventually leading stability and control education and research in that country Pioneer stability and control educators in continental Europe were the Belgian Professor Frederic Charles Haus, the Dutch Professor Otto H. Gerlach, and the German Professor Karl-H. Doetsch.

Airplane stability and control is still being taught in universities around the world, bring­ing fresh talent into the field. Stability and control research is carried on in many of these schools, usually as graduate programs. Governmental and commercial research institutions are important contributors, as well.

Photographs of some stability and control educators and engineers who are mentioned in the text appear in Figure 2.1.