Category Airplane Stability and Control, Second Edition

Ultralight Airplane Pitch Stability

Conventional ideas about the need for longitudinal static stability are misleading in the case of ultralight airplanes. The reason is that, instead of the normal short – and long – period, or phugoid, modes of motion, four unfamiliar first-order modes may appear. For ex­ample, the Gossamer Condor’s center of gravity is aft of the neutral point, in order to unload somewhat the canard surface. This produces a positive or unstable value for the CMa deriva­tive. As a result, one of the four first-order modes is unstable. However, the corresponding divergence has a time constant of about 1,000 seconds, making it imperceptible to pilots.

Another way to explain the benign pitch behavior of ultralight airplanes flying at centers of gravity behind the neutral point is to consider their maneuvering stability. Maneuvering stability disappears at the maneuver point. The maneuver point of ultralight airplanes tends to be far aft of the neutral point because of high pitch and heave damping levels. For flight at centers of gravity behind the neutral point but ahead of the maneuver point, the machine would have no tendency to diverge unstably in pitch attitude at constant airspeed. Its unstable behavior would require a simultaneous loss of airspeed and nose-up pitch change in level flight, a process that is very slow.

To illustrate the concept of the maneuver point or maneuvering stability, consider an airplane with an unstable gradient in pitching moment with angle of attack, and suppose it to be disturbed nose-up with respect to its flight path. The unstable pitching moment gradient would tend to increase the size of the disturbance, but at the same time the increase of angle of attack would cause the flight path to curve upward if the speed is constant. The upward curvature of the flight path implies an angular velocity in pitch, which is resisted by the aerodynamic damping in pitch.

In the case of the Gossamer aircraft, the stabilizing effect of the pitch damping due to flight path curvature overwhelms the destabilizing gradient of pitching moment with angle of attack. The neutral point is 5 percent ahead of the center of gravity, but the maneuver point is four chord lengths behind the center of gravity, due to the large path curvature for a given angle of attack.

The Oblique or Skewed Wing

Another rotation-only variable-sweep concept was invented by the late Robert T. Jones at the NACA Ames Aeronautical Laboratory, around 1945 (Figure 16.3). This is the oblique or skewed wing, in which wing sweepback (and sweepforward) is achieved by rotating the wing at its center, sweeping one side back and the other side forward. With the oblique wing rotated back into symmetry, the configuration avoids the tip stalling and low-speed stability and control problems associated with ordinary wing sweepback. Jones’ invention seems to have paralleled other rotating-wing sweep concepts, those of Lachmann of Handley Page and Richard Vogt of Blohm and Voss. Jones expected an additional advantage for the oblique wing as compared with conventionally swept wings, that of higher supersonic lift-drag ratio.

Had the unorthodox oblique-winged configuration been proposed by someone without Jones’ immense prestige, it might have been dismissed at once. But, for one thing, Robert Jones was credited with the invention of wing sweepback to alleviate compressibility ef­fects during World War II, independently of the Germans. He also contributed largely to stability and control theory, in all-movable controls, lateral control, two-control airplanes, and in solutions of equations of motion. Like the Wright brothers, Edward Heinemann, and John Northrop, Jones was not university-trained. His considerable mathematics were self-taught.

With the wing rotated, the oblique-wing configuration is that rarest of heavier-than-air machines, one without bilateral or mirror-image left-right symmetry Birds, dragonflies, and our own flying creations all have bilateral symmetry, as we ourselves do. It seems obvious that the flying qualities of an oblique-winged airplane would be strange, if not dangerous. For one thing, pulling up the airplane’s nose to increase angle of attack would create inertial rolling and yawing moments, quite absent in symmetrical airplanes. These moments arise from pitching velocity and acceleration acting on a nonzero product of inertia term Ixy.

The Oblique or Skewed Wing

Figure 16.3 Robert T. Jones, ahead of his time in many areas of aeronautics. He was the inventor in the United States of wing sweepback and of the oblique-winged airplane. Jones contributed to stability and control theory in lateral control, in two-control airplanes, and in all-movable controls. (From Hansen, Engineer in Charge, 1987)

The effectiveness of trailing-edge flap-type controls is seriously reduced at large sweep or skew angles. Control deficiencies can be made up if the airplane carries conventional tail surfaces. Control problems are more critical if an oblique wing airplane is always operated in the skewed position, but this would obviate the need for rotating engine pods and vertical tail surfaces.

Wing torsional divergence on the sweptforward panel, discussed in Chapter 19, “The Elastic Airplane,” has been raised as an issue for the oblique wing. Jones quite early predicted that rigid-body roll freedom would tend to raise the divergence speed to safe values outside of the flight range. That is, when the leading or sweptforward panel starts to bend upward under high airloads, the lift on that panel would increase, causing a large rolling moment. Airplane roll response to that moment would alleviate the airload and the wing would be safe.

However, the case must be considered in which automatic roll control operates to hold the airplane at zero bank. If the control rolling moment that holds the zero-bank angle comes from a horizontal tail, the wing torsional divergence speed could be close to the body-clamped case. A free-free analysis that includes autopilot loops would seem to be needed. On the other hand, if control rolling moment comes from ailerons on the leading panel, the panel loads would be reduced, as in the case of free-body roll. This would raise torsional divergence speed above the body-clamped value.

Some detailed stability and control data on oblique wings were obtained in NASA Ames Research Center wind-tunnel tests and in a NASA-Navy funded study begun in 1984. The

The Oblique or Skewed Wing

Figure 16.4 Zero-sideslip variations of rolling moment and side force coefficients for an oblique wing tested on a model of the NASA-Vought F-8 research airplane. Sizable, nonlinear values appear for wing skew angles of 30 degrees and above. (From Kroo, AIAA Short Course Notes, 1992)

 

study was on the feasibility of converting NASA’s F-8 Digital Fly-By-Wire Airplane to an oblique wing configuration. A key problem surfaced in the unusual nonlinear variations at zero sideslip angle in side force, and rolling and yawing moments with angle of attack, at wing skew angles as low as 30 degrees (Figure 16.4). These are trim moments, which would have to be trimmed out by control surface deflections for normal, nonmaneuvering flight. The nonzero side force could be equilibrated by flying at a steady bank angle, or possibly by wing tilt with respect to the fuselage.

Other possibilities to deal with nonzero side forces, yawing, and rolling moments at zero sideslip include wing plan form adjustments, unsymmetrical tip shaping, wing pivot selection, antisymmetric wing twist, and variable tip dihedral (Kroo, 1992). One is left with the impression that the aerodynamic design of a practical oblique-wing airplane will be far more complex than for its swept-wing counterpart.

There have been a number of oblique-wing flight tests, starting with a test in the Langley Research Center’s Free Flight Wind Tunnel. R. T. Jones also built and successfully flew a

The Oblique or Skewed Wing

Figure 16.5 The R. T. Jones invention in flight, the Ames-Dryden AD-1 oblique-wing testbed, flying with its adjustable wing in the fully swept 60-degree position. (From Hallion, NASA SP-4303, 1984)

The Oblique or Skewed Wing

Figure 16.6 The Vickers-Armstrong “Swallow” variable-sweep concept, tested at NASA’s Langley Laboratory and found to be longitudinally unstable with wings unswept. (From Polhamus and Toll,

NASA TM 83121, 1981)

series of small free-flying oblique-winged model aircraft, culminating in a radio-controlled two-meter span model whose wing andtailplane skew angle could be systematically changed in flight. A considerable number of oblique-wing design studies followed. NASA eventually contracted to have a full-scale oblique-wing test airplane built for low-speed flight tests. This airplane, the AD-1, a single-engine jet, was flown successfully at the NASA Dryden Flight Research Center at Edwards, California (Figure 16.5). Ten degrees of bank angle on the AD-1 are required to cancel the side force produced by a 60-degree wing skew angle (Kroo, 1992).

The Dryden flight tests were followed by a NASA design research contract for an oblique­wing supersonic transport. The contract was awarded to Boeing, McDonnell-Douglas, and Kansas University, around 1992. The study revealed arrangement problems with that partic­ular arrangement. An all-wing version of the oblique-wing eliminates the need for hinging the wing to a fuselage, although engine pods and any vertical tails still require hinging. Another NASA design research contract to Stanford University is for a flying model of a 400-foot-span all-wing supersonic transport, operated as an oblique wing. Stability and control for the all-wing versions of the oblique wing are problematic because of the problem of nonzero side forces, rolling, and yawing moments in oblique cruising flight.

The Semirigid Approach to Wing Torsional Divergence

In the semirigid approach to wing torsional divergence and related problems a reference section of the wing is selected to represent the entire three-dimensional wing. This simplification works quite well for slender wings, that is, wings of high-aspect ratio.

Semirigid analyses of wing torsional divergence are given in a number of textbooks (for example, Duncan, 1943; Fung, 1955). Fung shows a wing section that rotates about a pivot and is acted upon by a lift load. The pivot represents the chordwise location in the section of the wing’s elastic axis, or location where lift loads will not produce twist. The lift load can be taken as acting through the section’s aerodynamic center. The aerodynamic center, near the section’s quarter-chord point, is the point about which section pitching moments are invariant with angle of attack (Figure 19.1).

The wing section will come to a static equilibrium angle at some angle of attack under the combined action of the lift load and a spring restraint about the pivot. The spring restraint represents the wing’s elastic stiffness. If the pivot, representing the elastic axis, is behind

The Semirigid Approach to Wing Torsional Divergence

Figure 19.1 Semirigid model forwingtorsional divergence. Thewingis replacedby atypical section, pivoted aboutapoint that represents the wing’s elastic axis. The spring represents elastic stiffness. Inthis illustration, the wing’s aerodynamic center, where the lift acts, is forward of the pivot point. Increasing airspeed eventually leads to a torsional divergence. The angle of attack a increases without limit. (From Fung, The Theory of Aeroelasticity, Dover, 1969)

the wing’s aerodynamic center, the equilibrium angle of attack increases with increasing airspeed, which gives higher wing lift loads.

For any eccentricity, or distance of the aerodynamic center ahead of the pivot, and for given spring constants and wing lift curve slopes, or variations of wing lift with angle of attack, there is an airspeed at which the semirigid model diverges. That is, the equilibrium solution fails. Twist angle and angle of attack increase without limit. This is the calculated wing torsional divergence speed.

Wing torsional divergence problems were encountered on the Republic F-84 and Northrop F-89 airplanes, both equipped with large tip tanks (Phillips, 1998). Fixed fins on the outside rear of the F-84’s tanks moved the wing’s aerodynamic center aft, eliminating the problem.

Linear Quadratic Gaussian Controllers

Linear quadratic Gaussian (LQG) controllers add to the linear quadratic (LQ) designs random disturbances and measurement errors. LQG designs are discussed at length in a 1986 text and a 1993 IEEE paper by Professor Robert F. Stengel. The form taken by

Linear Quadratic Gaussian Controllers

Figure 20.8 Various control system forms that can be represented with the structured linear quadratic regulator(LQG)method. (FromStengel, IEEE Trans. onSystems, Man, andCybernetics, © 1993 IEEE)

the discrete-time LQG optimal controller is

uk = CFyk* – CBxk,

where yk * is the desired value of an output vector and xk is the Kalman filter state estimate.

The LQG design approach is very flexible because of the number of parameters that can be chosen arbitrarily. At one extreme, a scalar one-input, one-output design can be produced. Measurement and control redundancies can be represented if measurement and control vector sizes exceed that of the state vector. Also, integral compensation and explicit model-following structures can be produced (Figure 20.8).

LQG designs are among the most advanced to be in use by stability-augmentation en­gineers, as this is written. Even more advanced control concepts continue to pour out of university and other research centers. The same 1993 paper by Stengel cited above provides a good survey of advanced control concepts, including expert systems, neural networks, and intentionally nonlinear controls.

20.3 Failed Applications of Optimal Control

The failure of optimal control methods to produce a satisfactory flight control system for the Grumman X-29A airplane was noted in Sec. 14. This failure is by no means an isolated event. Additional instances can be found in which optimal control methods in the hands of experienced engineers have failed to produce safe and satisfactory flight control systems. What has gone wrong? Several experts who have witnessed these failures discuss the problem:

Phillip R. Chandler and David W. Potts (1983), U. S. Air Force Flight Dynamics Laboratory “[T]he infinite bandwidth constant compensation elements which are required [for LQR] violate the very heart of the feedback problem. . . . LQR therefore is an elegant mathematical solution to a nonengi­neering problem SVT (Singular Value Theory) [Doyle, 1979] is a very crude

method of coping with uncertainty in the LQR or LQG procedure. It makes assumptions that are not valid for flight control_______________________________________ LQR with all its ramifica­

tions and refinements is totally unsuited for the flight control servomechanism problem.”

John C. Gibson (2000), formerly with English/Electric/British Aerospace

“[Robert J.] Woodcock told me that there have been several missile and aircraft projects in serious trouble due to the use of such [LQG] methods_______________________________________ While op­

timization methods are continually being improved, they cannot yet (and may never) guarantee a safe and satisfactory FCS [flight control system] design with­out the strictest guidance and detailed physical understanding of experienced control and handling qualities engineers. This is true for highly advanced and demanding types of aircraft. Every signal path must be clearly visible and eas­ily related to specific aerodynamic or inertial characteristics of the airframe. In simple aircraft without complexity, there is no advantage over straightforward engineering methods anyway.”

Michael V. Cook (1999, 2000), Senior Lecturer, Cranfield University “There exists an enormous wealth of published material describing the application of so-called, ‘modern control methods’ to the design of flight control systems for piloted aeroplanes. It is also evident, with the exception of a very small number of recent applications, that there is a conspicuous lack of enthusiasm on the part of the airframe manufacturers to adopt this design technology, especially for the design of command and stability augmentation systems for piloted airplanes. Having an industrial background I am well aware of the many reasons why modern control has not been taken onboard seriously by the manufacturers – academic control specialists don’t share my view, and in many cases probably don’t even understand it!… I know that my views are shared by the control

people in——- who, in private are not at all complimentary about the academic

control specialists in the UK. I am also aware that the Boeing view is similar to

that of—— . I’ve seen some appallingly bad control systems design theses (not

from Cranfield).”

Steven Osder (2000), Osder Associates, Arizona “We [Osder and Dunstan Graham] used to lament the absurdity of papers [on robustness theory] that were filling the journals and we amused each other by citing specific examples of such departures from reason and logic_____________________ At the [Boeing] helicopter com­

pany, we took each of those University of – [robust flight control] designs and tested them against more complete [nonlinear] models of the [Apache] aircraft.

In every case, these robust flight control designs always fell out of the sky. In one case [which used eigenstructure assignment], even testing against a lin­ear model, but with only a 10 percent variation in a single B [control] matrix term, our simulations resulted in a crash.”

Duane T. McRuer (2001), Chairman, Systems Technology, Inc. “At STI we have spent an enormous amount of time and effort searching for ways to make optimal control practical – at least 20 major reports and papers, with some tremendously capable folk (e. g., Dick Whitbeck, Greg Hofmann, Bob Stapleford, Peter Thompson, et al.). Our focus has been on finding performance indices, special schemes, etc., to make optimal control solutions jibe with good

design practice__ We have just never been happy with the results for stability

augmentation design.”

In the light of the foregoing comments, a design case (Ward, 1996) in which an LQG design for a pitch stability augmentation system was used only as a guideline for a more conventional approach suggests a reasonable use for optimal control techniques. The concept of using LQR optimal control synthesis as a guide or in conjunction with classical methods is also developed by Blight (1996). Blight also comments that LQR methods should be used only on “control problems that actually require modern multivariable methods for their solution.” For example, Blight recommends ordinary gain scheduling instead of attempting to design a single robust linear control law for all flight conditions.

Preface

After raising student enthusiasm by a particularly inspiring airplane stability and control lecture, Professor Otto Koppen would restore perspective by saying, “Remember, airplanes are not built to demonstrate stability and control, but to carry things from one place to another.” Perhaps Koppen went too far, because history has shown over and over again that neglect of stability and control fundamentals has brought otherwise excellent aircraft projects down, sometimes literally. Every aspiring airplane builder sees the need intuitively for sturdy structures and adequate propulsive power. But badly located centers of gravity and inadequate rudder area for spin recovery, for example, are subtleties that can be missed easily, and have been missed repeatedly.

Before the gas turbine age, much of the art of stability and control design was devoted to making airplanes that flew themselves for minutes at a time in calm air, and responded gracefully to the hands and feet of the pilot when changes in course or altitude were required. These virtues were called flying qualities. They were codified for the first time by the National Advisory Committee for Aeronautics, the NACA, in 1943. Military procurement specifications based on NACA’s work followed two years later.

When gas turbine power arrived, considerations of fuel economy drove airplanes into the stratosphere and increased power made transonic flight possible. Satisfactory flying qualities no longer could be achieved by a combination of airplane geometry and restric­tions on center-of-gravity location. Artificial stability augmenters such as pitch and yaw dampers were required, together with Mach trim compensators, all-moving tailplanes, and irreversible surface position actuators. At roughly the same time, the Boeing B-47 and the Northrop B-49 and their successful stability augmenters marked the beginning of a new age.

Since then much of the art and science that connected airplane geometry to good low – altitude flying qualities have begun to be lost to a new generation of airplane designers and builders. The time has come to record the lore of earlier airplane designers for the benefit of the kit-built airplane movement, to say nothing of the survivors of the general-aviation industry. Accordingly, this book is an informal, popular survey of the art and science of airplane stability and control. As history, the growth of understanding of the subject is traced from the pre-Wright brothers’ days up to the present. But there is also the intention of preserving for future designers the hard-won experience of what works and what doesn’t. The purpose is not only to honor the scientists and engineers who invented airplane stability and control, but also to help a few future airplane designers along the path to success.

If this work has any unifying theme, it is the lag of stability and control practice behind currently available theory. Repeatedly, airplanes have been built with undesirable or even fatal stability and control characteristics out of simple ignorance of the possibility of using better designs. In only a few periods, such as the time of the first flights near the speed of sound, theoreticians, researchers, and airplane designers were all in the same boat, all learning together.

The second edition of this book brings the subject up to date by including recent de­velopments. We have also used the opportunity to react to the numerous reviews of the first edition and to the comments of readers. One theme found in many reviews was that the first edition had neglected important airplane stability and control work that took place outside of the United States. That was not intentional, but the second edition has given the authors a new opportunity to correct the problem. In that effort, we were greatly aided by the following correspondents and reviewers in Canada, Europe, and Asia: Michael V Cook, Dr. Bernard Etkin, Dr. Peter G. Hamel, Dr. John C. Gibson, Bill Gunston, Dr. Norohito Goto, Dr. Gareth D. Padfield, Miss A. Jean Ross, the late Dr. H. H. B. M. Thomas, and Dr. Jean-Claude L. Wanner.

The interesting history of airplane stability and control has not lacked for attention in the past. A number of distinguished authors have presented short airplane stability and control histories, as distinct from histories of general aeronautics. We acknowledge particularly the following accounts:

Progress in Dynamic Stability and Control Research, by William F. Milliken, Jr., in the September 1947 Journal of the Aeronautical Sciences.

Development of Airplane Stability and Control Technology, by Courtland D. Perkins, in the July-August 1970 Journal of Aircraft.

Eighty Years of Flight Control: Triumphs and Pitfalls of the Systems Approach, by Duane T McRuer and F. Dunstan Graham, in the July-August 1981 Journal of Guidance and Control.

Twenty-Five Years of Handling Qualities Research, by Irving L. Ashkenas, in the May 1984 Journal of Aircraft.

Flying Qualities from Early Airplanes to the Space Shuttle, by William H. Phillips, in the July-August 1989 Journal of Guidance, Control, and Dynamics.

Establishment of Design Requirements: Flying Qualities Specifications for Amer­ican Aircraft, 1918-1943, by Walter C. Vincenti, Chapter 3 of What Engineers Know and How They Know It, Johns Hopkins University Press, 1990.

Evolution of Airplane Stability and Control: A Designer’s Viewpoint, by Jan Roskam, in the May-June 1991 Journal of Guidance.

Recollections of Langley in the Forties, by W. Hewitt Phillips, in the Summer 1992 Journal of the American Aviation Historical Society.

Many active and retired contributors to the stability and control field were interviewed for this book; some provided valuable references and even more valuable advice to the authors. The authors wish to acknowledge particularly the generous help of a number of them. Perhaps foremost in this group was the late Charles B. Westbrook, a well-known stability and control figure. Westbrook helped with his broad knowledge of U. S. Air Force – sponsored research and came up with several obscure but useful documents. W. Hewitt Phillips, an important figure in the stability and control field, reviewed in detail several book chapters. His comments are quoted verbatim in a number of places. Phillips is now a Distinguished Research Associate at the NASA Langley Research Center.

We were fortunate to have detailed reviewsfrom two additional experts, William H. Cook, formerly of the Boeing Company, and Duane T. McRuer, chairman of Systems Technology, Inc. Their insights into important issues are used and also quoted verbatim in several places in the book. Drs. John C. Gibson, formerly of English Electric/British Aerospace, and Peter G. Hamel, director of the DVL Institute of Flight Research, Braunschweig, were helpful with historical and recent European developments, as were several other European and Canadian engineers.

Jean Anderson, head librarian of the Guggenheim Aeronautical Laboratory at the California Institute of Technology (GALCIT) guided the authorsthrough GALCIT’simpres – sive aeronautical collections. All National Advisory Committee for Aeronautics (NACA) documents are there, in microfiche. The GALCIT collections are now located at the Institute’s Fairchild Library, where the Technical Reference Librarian, Louisa C. Toot, has been most helpful. We were fortunate also to have free access to the extensive stability and control collections at Systems Technology, Inc., of Hawthorne, California. We thank STI’s chairman and president, Duane T. McRuer and R. Wade Allen, for this and for very helpful advice.

The engineering libraries of the University of California, Los Angeles, and of the University of Southern California were useful in this project. We acknowledge also the help of George Kirkman, the volunteer curator of the library of the Museum of Flying, in Santa Monica, California, and the NASA Archivist Lee D. Saegesser.

In addition to the European and Asian engineers noted previously, the following people generously answered our questions and in many cases loaned us documents that added materially to this work: Paul H. Anderson, James G. Batterson, James S. Bowman, Jr., Robert W. Bratt, Daniel P. Byrnes, C. Richard Cantrell, William H. Cook, Dr. Eugene E. Covert, Dr. Fred E. C. Culick, Sean G. Day, Orville R. Dunn, Karl S. Forsstrom, Richard G. Fuller, Ervin R. Heald, Robert K. Heffley, Dr. Harry J. Heimer, R. Richard Heppe, Bruce E. Jackson, Henry R. Jex, Juri Kalviste, Charles H. King, Jr., William Koven, David A. Lednicer, Dr. Paul B. MacCready, Robert H. Maskrey, Dr. Charles McCutchen, Duane T McRuer, Allen Y. Murakoshi, Albert F. Myers, Dr. Gawad Nagati, Stephen Osder, Robert O. Rahn, Dr. William P Rodden, Dr. Jan Roskam, Edward S. Rutowski, George S. Schairer, Roger D. Schaufele, Arno E. Schelhorn, Lawrence J. Schilling, Dr. Irving C. Statler, and Dr. Terrence A. Weisshaar.

Only a few of these reviewers saw the entire book in draft form, so the authors are responsible for any uncorrected errors and omissions.

This book is arranged only roughly in chronological order. Most of the chapters are thematic, dealing with a single subject over its entire history. References are grouped by chapters at the end of the book. These have been expanded to form an abbreviated or core air­plane stability and control bibliography. The rapid progress in computerized bibliographies makes anachronistic a really comprehensive airplane stability and control bibliography.

Malcolm J. Abzug E. Eugene Larrabee

Airplane Stability and Control, Second Edition

Power Effects on Stability and Control

The World War II period 1939-1945 coincided almost exactly with the appearance of power effects as a major stability and control problem. Grumman Navy fighters of that period illustrate the situation. World War II opened with the F4F Wildcat as the Navy’s first-line fighter and ended with the debut of the F8F Bearcat. The external dimensions of the two aircraft were almost identical, but the F8F’s engine was rated at 2,400 horsepower, compared to 1,350 horsepower for the F4F.

In unpublished correspondence, W Hewitt Phillips remarks that the appearance of power effects as a major stability and control problem was not entirely the result of growth in engine power:

these effects have been with us since World War I, but weren’t serious then because of the light control forces required to offset these effects, resulting from the low speeds and smaller size of these airplanes. The power effects in terms of thrust and moment coefficients were probably of the same order as in the case of the World War II fighters. These effects would have been somewhat reduced because of the short nose moment arm of these planes, and because of the lower lift coefficients due to the lack of high lift flaps.

The further growth in power and stability effects on military propeller-driven aircraft was of course interrupted by the advent of jets, with a different set of power effects on stability and control, generally of a minor nature. This chapter reviews the history of both propeller and jet power effects on stability and control. Although the days of high-powered propeller-driven military aircraft may be ended, their civil counterparts still exist, with a new set of stability and control problems.

Artificial Feel Systems

Since irreversible power controls isolate the pilot from aerodynamic hinge moments, artificial restoration of the hinge moments, or “artificial feel,” is required.

Longitudinal artificial feel systems range in complexity from simple springs, weights, and stick dampers to computer-generated reactive forces applied to the control column by servos.

A particularly simple artificial feel system element is the bobweight. The bobweight introduces mass unbalance into the control circuit, in addition to the unbalances inherent in the basic design. That is, even mass-balanced mechanical control circuits have inertia that tends to keep the control sticks, cables, and brackets fixed while the airplane accelerates around them. Bobweights are designed to add the unbalance, creating artificial pilot forces proportional to airplane linear and angular accelerations. They also have been used on airplanes without irreversible power controls, such as the Spitfire and P-51D.

The most common bobweight form is a simple weight attached to a bracket in front of the control stick. Positive normal acceleration, as in a pullup, requires pilot pull force to overcome the moment about the stick pivot of increased downward force acting on the bobweight. There is an additional pilot pull force required during pullup initiation, while the airplane experiences pitching acceleration. The additional pull force arises from pitch­ing acceleration times the arm from the center of gravity to the bobweight. Without the pitching acceleration component, the pilot could get excessive back-stick motions before the normal acceleration builds up and tends to pull the stick forward.

In the case of the McDonnell Douglas A-4 airplane’s bobweight installation, an increased pitching acceleration component is needed to overcome overcontrol tendencies at high airspeeds and low altitudes. A second, reversed bobweight is installed at the rear of the airplane. The reversed bobweight reduces the normal acceleration component of stick force but increases the pitching acceleration component.

Another interesting artificial feel system element is the q-spring. As applied to the Boeing XB-47 rudder (White, 1950) the q-spring provides pedal forces proportional to both pedal deflection and airplane dynamic pressure, or q. Total pressure (dynamic plus static) is put into a sealed container having a bellows at one end. The bellows is equilibrated by static pressure external to the sealed container and by tension in a cable, producing a cable force proportional to the pressure difference, or q. Pilot control motion moves an attachment point of that cable laterally, providing a restoring moment proportional to control motion and to dynamic pressure.

It appears that a q-spring artificial feel system was first used on the Northop XB-35 and B-49 flying wing elevons, combined with a bobweight. Q-spring artificial feel sys­tem versions have survived to be used on modern aircraft, such as the elevators of the Boeing 727, 747, and 767; the English Electric Lightning; and the McDonnell Douglas DC-10. Hydraulic rather than pneumatic springs are used, with hydraulic pressure made proportional to dynamic pressure by a regulator valve. In many transport airplanes the force gradient is further modulated by trim stabilizer angle. Stabilizer angle modulation, acting through a cam, provides a rough correction for the center of gravity position, reducing the spring force gradient at forward center of gravity positions. Other modulations can be introduced.

Advanced artificial feel systems are able to modify stick spring and damper character­istics in accordance with a computer program, or even to apply forces to the stick with computer-controlled servos.

Advent of the Free-Spinning Wind Tunnels

NACA research on airplane spinning began about the year 1926 (Zimmerman, 1936). At first, dynamically scaled airplane models were launched from the top of a balloon shed and observed as they fell. Hartley A. Soule and N. A. Scudder are associated with these early tests. Similar work went on in Britain at that time. A. V Stephens writes (1966):

The technique of using balsa wood [drop] models for spinning research had originated in America and had promptly been abandoned. It was taken up at the Royal Aircraft Estab­lishment [RAE] by K. V Wright and the author, who launched the models from the catwalk

Advent of the Free-Spinning Wind Tunnels

Подпись: Figure 9.1 Exterior and cross-sectional views of the NASA Langley 20-Foot Free-Spinning Wind Tunnel, built in 1941. (From Neihouse, Klinar, and Scher, NASA Rept. R-57, 1960)

in the roof of the balloon shed and observed their fall. Just as the technique was beginning to yield useful results it was decided to demolish the balloon shed. At this point R. McKinnon Wood put forward a characteristically original suggestion that such experiments could be done in a large vertical wind tunnel. Pessimists argued that the models would immediately run into the tunnel walls, but it was soon demonstrated in a model tunnel that in fact they had a slight tendency to keep away.

Drop models were to make a comeback when helicopters became available, but in the early days, aside from the destruction of the RAE balloon shed, the limited test times in free drops from buildings were a severe handicap. McKinnon Wood’s vertical wind tunnel got around the limited test time problem. The RAE model tunnel worked so well that Stephens had a 12-foot-diameter vertical tunnel built, which saw years of service.

The first NACA spin tunnel, built in 1935, had a 5-foot diameter. It was used by Millard J. Bamber and R. O. House, in addition to Charles Zimmerman. Force and moment mea­surements on a rotary balance could be taken in this little tunnel, in addition to free-spinning tests. However, when a new 15-foot free-spinning wind tunnel was opened in 1936, there was no rotary balance.

The current 20-foot NASA Spin Tunnel dates from 1941 (Figure 9.1). There were com­parable vertical wind tunnels built at Wright Field, at IMFL in France, at TRDI in Japan, at the National Research Laboratories of Canada, and at the RAE in Britain. There is even a privately owned spin tunnel in the woods near Neuburg, Germany, operated by Bihrle Applied Research. The balsa and spruce spin models covered with silk tissue paper used in the early days have given way to sturdier vacuum-formed plastic and fiberglass scale models. However, a visitor to any of the modern spin tunnels is aware of a difference from the heavy industry feeling of an ordinary large wind tunnel. Models are launched from a balcony at the top of the tunnel structure and are recovered into nets strung around the bottom. Damaged models are frequently patched and reused.

The free-spinning wind tunnels are essentially analog computers. Their main use is for the study of developed spins and the recovery from developed spins. Models are launched into spin tunnels by hand, with a sort of Frisbee skimming motion. When the initial launch transient has died away, the model is expected to settle into the fully developed erect or inverted, steady or oscillatory, spin for which it is trimmed (Figure 9.2). A clockwork or radio-controlled mechanism applies preprogrammed spin recovery controls or deploys a spin chute. A chief result is the number of turns required before recovery, if there is a recovery, but other parameters are measured as well (Figure 9.3).

An interesting concept of “satisfactory recovery” emerged from the NACA spin tunnel experience. This accounts for the human factor by requiring that recovery into unstalled, straight flight takes no more than 2 1/4 turns after recovery controls are applied. The reasoning is that pilots cannot be expected to stay with what their handbook tells them is the correct recovery procedure after that many turns, but will try something else or leave the airplane if they have parachutes or ejection seats. An additional bow to the human factor in defining satisfactory recovery in the spin tunnel is to use no more than two-thirds of full control travel in the recovery sense.

Spin tunnels are valuable in that aerodynamic forces and moments are correctly rep­resented at large values of angles of attack and sideslip and airplane angular velocities, except of course for scale and compressibility effects. This is no small consideration. Those researchers who try to avoid the use of spin tunnels because of scale or compressibility effects, or to supplement spin tunnels by calculating spinning motions on digital com­puters, face formidable data base problems, of which we will discuss more later. Where

Advent of the Free-Spinning Wind Tunnels

Figure 9.2 Model spinning in the test section of the NASA 20-Foot Free-Spinning Wind Tunnel.

(From Neihouse, Klinar, and Scher, NASA Rept. R-57, 1960)

spin entry characteristics are an important consideration or fully developed spins are not expected, dropped models are favored over spin tunnels.

Invention of the Sweptback Wing

The story of the independent invention of the sweptback wing in the United States by Robert T. Jones and in Germany by Adolph Busemann has been told many times. But some accounts of the early work on the stability and control effects of wing sweep belong to this history.

The dive pullout problems of thick, straight-wing airplanes such as the Lockheed P-38 were mainly due to a large increase in static longitudinal stability at high Mach numbers. Thus, an early theoretical result (Jones, 1946) seemed too good to be true. Jones showed that the static longitudinal stability or aerodynamic center location of sharply swept delta wings is invariant with Mach number, from zero to supersonic speeds. A test of a triangular wing of aspect ratio 0.75, with leading-edge sweep of 79 degrees, confirmed the theory. The catch turned out to be that wings of that low aspect ratio are impractical for airplanes that operate out of normal airports.

More practical swept wings for airplanes have higher aspect ratios. In moderately high – aspect-ratio-swept wings there is an outboard shift in additional span loading (Figure 11.7). The outboard shift in additional span load leads to wing tip stall at low angles of attack for moderate – to high-aspect-ratio-swept wings. Outflow of the boundary layer adds to this tendency. Wing tip stall causes an unstable break in the wing pitching moment at the stall (Figure 11.8). That is, loss of lift behind the center of gravity causes the wing (and airplane) to pitch nose-up at the stall, driving the airplane deeper into stall. On the other hand, a stable pitching moment break or nose-down pitch leads to stall recovery, provided that the elevator is moved to trim at a lower angle of attack. Tip stall also leads to an undesirable wing drop and reversal or positive signs for the roll damping derivative Clp, making spins easier to enter and sustain. A condition for autorotation in spins is a positive Clp.

The situation changes for low-aspect-ratio-swept wings, where leading-edge vortex flow acts to create diving, or stabilizing, pitching moments at the stall. A striking correlation was produced showing the combinations of wing sweep and aspect ratio that produce either stable or unstable pitching moment breaks at the stall (Shortal and Maggin, 1946). Figure

11.9 shows an extended version that includes taper ratio effects (Furlong and McHugh, 1957). The stable region was shown to be broadened for sharply tapered wings.

The McDonnell-Douglas F-4 Phantom’s wing, with aspect ratio 2.0 and quarter-chord sweep of 45 degrees, is precisely on the Shortal-Maggin stability boundary, signifying a neu­tral pitching moment break at the stall. High-aspect-ratio-swept wings, typical of transport

Invention of the Sweptback Wing

Figure 11.7 The outward shift in additional span load distribution caused by using wing sweepback. Load increases at the tip at high angles of attack, leading to tip stalling. (From Furlong and McHugh, NACA Rept. 1339, 1957)

 

Invention of the Sweptback Wing

Figure 11.8 The effect of sweepback on the pitching moment coefficient break at the stall. The straight and 15-degree swept wings are stable beyond the stall; the 30-degree swept wing is unstable (noses up). (From Furlong and McHugh, NACA Rept. 1339, 1957)

 

.(Ref. 10)

Invention of the Sweptback Wing

0 20 40 60 80

Лс/4, deg

Figure 11.9 Shortal and Maggin’s celebrated empirical longitudinal stability boundary for sweptback wings, extended to include the effect of taper ratio. (From Furlong and McHugh, NACA Rept. 1339, 1957)

airplanes, are unstable at the stall without auxiliary devices. For example, the Lockheed 1011’s wing, with aspect ratio 6.95 and quarter-chord sweep of 35 degrees, is in the un­stable zone at the stall. An early attempt to evaluate in-flight the low-speed stability and control characteristics of moderate-aspect-ratio-swept wing airplanes was made by sim­ply removing the wings of a Bell P-63 Kingcobra and reattaching them to the fuselage at a sweep angle of 35 degrees. The tail length was increased at the same time by adding a constant cross-section plug to the fuselage aft of the wing trailing edge. NACA called this early research airplane the L-39. The L-39’s first flight was made by A. M. (Tex) Johnston. He was to become famous a few years later as the test pilot for Boeing’s prototype 707 jet airliner.

Wind-tunnel tests of the L-39 showed the usual increase in dihedral effect with increasing angle of attack. That is, the rolling moment coefficient in sideslip becomes quite high in the stable direction at attitudes near the stall. There was real concern on the L-39 that if sideslip angles occurred during liftoff or the landing flare, as a result of gusts or rudder use for cross-wind corrections, the rolling moment from dihedral effects would quite overpower the ailerons and the airplane would roll out of control.

This dire possibility was part of the preflight briefing for the pilot Johnston. A briefer, one of this book’s authors (Abzug), remembers that Johnston showed no reaction and asked no questions about this, showing a bit more than the usual test pilot self-confidence. All turned out well. The L-39 flight tests were reasonably routine, and sweptback wings for the next generation of commercial and military jets were on their way.

14.8.3 Modern Identification Methods

The higher powered stability derivative extraction schemes that followed knob twisting engage the interest of many mathematically minded people in the stability and control community. The focus has been broadened beyond the linearized stability deriva­tives, and the subject is now usually called flight vehicle system identification. The years have seen centers of identification activity at individual laboratories, such as Calspan and the NASA Dryden Flight Research Center, and any number of university graduate students earning doctoral degrees in this area. Kenneth W. Iliff and Richard E. Maine at Dryden are leaders in the identification field in the United States.

The DLR Institute in Braunschweig is particularly active in this area, under the guidance of Dr. Peter Hamel. The state of the art up to 1995 is summarized in a paper having 183 references by Drs. Hamel and Jategaonkar (1996). This summary has been updated (Hamel and Jategaonkar, 1999). A generalized model of the vehicle system identification process is shown in Figure 14.15.

A flow chart for a widely used method known as the maximum likelihood or output error method is given in Figure 14.16. The maximum likelihood method starts with a mathematical model of the airplane, which is nothing more than the linearized equations of airplane motion in state variable form (see Chapter 18). The method produces numerical values for the constants in those equations, the airplane’s dimensional stability and control derivatives. A cost function is constructed as the difference between measured and estimated responses, summed over a time history interval. Iliff describes the workings of the maximum likelihood method as follows (see Figure 14.16):

14.8.3 Modern Identification Methods

Figure 14.15 The generalized method of vehicle system identification. (From Hamel, RTO MP-11, 1999)

14.8.3 Modern Identification Methods

Figure 14.16 Flow chart for the maximum likelihood method of airplane stability and control deriva­tive extraction from flight test data. (From Iliff, Jour, of Guidance, Sept.-Oct. 1989)

The measured response is compared with the estimated response, and the difference be­tween these responses is called the response error. The cost functions… include this response error. The minimization algorithm is used to find the coefficient values that minimize the cost function. Each iteration of this algorithm provides a new estimate of the unknown coefficients on the basis of the response error. These new estimates of the coefficients are then used to update values of the coefficients of the mathematical model, providing a new estimated response and, therefore, a new response error. The up­dating of the mathematical model continues iteratively until a convergence criterion is satisfied.

At the time of this writing, the maximum likelihood method is the most widely used of the available identification techniques. For example, in 1993, R. V Jategaonkar, W. Monnich, D. Fischenberg, and B. Krag used this method at the DLR, Braunschweig, for the Transall airplane; and M. R. Napolitano, A. C. Paris, and B. A. Seanor used it at West Virginia University for the Cessna U-206 and McDonnell Douglas F/A-18 airplanes. In an ear­lier use at the NASA Dryden Flight Research Facility, Iliff, Maine, and Mary F. Schafer used maximum likelihood estimation to get a fairly complete set of stability and control derivatives for a Cessna T-37B and a 3/8-scale drop model of the McDonnell Douglas F-15.

Identification quality is dependent on the frequency content of the control input signal in Figure 14.16. Ideal control inputs would excite the system’s modes of motion that require control, while leaving unexcited higher frequencies representing measurement artifacts, such as vibration. Koehler (1977) at DLR devised a simple input with a relatively wide, but limited, frequency content. This is the 3211 signal. The 3211 refers to alternate positive and negative pulses of relative durations 3,2, 1, and 1. The DLR 3211 signal has become a standard in vehicle systems identification.

The alternate extended Kalman filter method of stability derivative extraction has the advantage of being suited to real-time operation. That is, it can be used as an element in a

14.8.3 Modern Identification Methods

Figure 14.17 Improvement of Cma identification on the X-31A with separate surface inputs. (From Weiss, Jour, of Aircraft, 1996)

closed-loop flight control system. Many of the applications of extended Kalman filtering imply or use this feature, as in the 1983 to 1991 work at Princeton University by M. Sri- Jayantha, Dennis J. Linse, and Robert F. Stengel.

A challenging area for identification is that of the aerodynamically unstable airframe, which can be flown only with full-time stability augmentation. Data scatter can be large in these cases, using current methods. Figure 14.17 shows that exciting motion with a separate control surface from that used for closed-loop control reduces identification data scatter.

Rotary derivatives and cross-derivatives, such as the rolling moment due to yawing and the yawing moment due to aileron deflection, are generally the least well-known data in the airplane equations of motion. Identification methods are at their worst for such parameters. Correlations of extracted derivatives with wind-tunnel and theoretical data generally focus on just those derivatives such as Clp and Clp whose numerical values are well known from other sources. Flight test data quality must be high for identification algorithms to work well, probably higher than needed for any other application. State noise from atmospheric turbulence and sensor noise are obvious complications.

The power of flight vehicle system identification continues to advance to the point where the derived system models can meet accuracy requirements for high-fidelity flight

14.8.3 Modern Identification Methods

Figure 14.18 Unsteady aerodynamic modeling of approach to stall, stall, and recovery on the Do 328 transport. Dots are flight test data; solid line is model output. (From Fischenberg and Jategaonkar, RTO MP-11, 1999)

simulators, such as those used in research and pilot training. Recent extensions of the theory include using the frequency domain in place of the usual time domain methods, and the application of neural networks.