Category Airplane Stability and Control, Second Edition

The crossover model has proved to be of great value in understanding pilot-induced oscillations. The way has been opened for validating empirical corrections for the phe­nomenon, such as described by Phillips, and for the development of new concepts in the area and superior flying qualities designs.

Duane McRuer provides a comprehensive survey of pilot-induced oscillations in a report for the Dryden Flight Research Center (McRuer, 1994). Having been experienced by the Wright brothers, pilot-induced oscillations qualify as the senior flying qualities problem. Recent dramatic flight experiences, combined with the availability of advanced analysis methods, have given the subject fresh interest. Between the years 1947 and 1994, there were over 30 very severe reported cases, in airplanes ranging from a NASA paraglider to the space shuttle Orbiter. McRuer proposes three pilot-induced oscillation categories, as follows:

essentially linear;

quasi-linear, with surface rate or position limiting;

essentially nonlinear, including pilot or mode transitions.

An important validation of the crossover model approach to the first category was furnished by analysis of fully developed pilot-induced oscillations on the USAF/Calspan variable-stability NT-33 (Bjorkman, 1986). In six severe cases there were large effective open-loop system delays, departing from the ideal integrator-type airframe transfer func­tion in the region of crossover (Figure 21.4). The required pilot dynamics for compensatory operation thus required

a great deal of pilot lead as well as exquisitely precise adjustment of pilot equalization and gain to approximate the crossover law and to close the loop in a stable manner.

Linear pilot-induced oscillations include complex interactions with airplane flexible modes. Mode-coupled oscillations have been experienced on the F-111, the YF-12, and the Rutan Voyager. Control surface rate-limiting pilot-induced oscillations were discussed previously.

Essentially nonlinear pilot-induced oscillations have arisen chiefly in connection with pilot and mode transitions. In one such case, weight-on-wheel and tail strike switches changed the stability augmentation control laws on the Vought/NASA fly-by-wire F-8, presenting the pilot with a rapid succession of different dynamics (McRuer, 1994). The pilot was unable to adapt in time. Mode transitions, either as a function of pilot input amplitude or automatic mode changes, are a particular source of pilot-induced oscillations in modern fly-by-wire flight control systems. The importance of avoiding pilot-induced oscillations on fly-by-wire transport airplanes led to the study discussed in Sec. 11.

From the first machines that flew for just minutes at a time to today’s sophisticated aircraft, stability and control have always been crucial considerations. Following up their successful first edition, Malcolm Abzug and Eugene Larrabee forge through to the present day with their informal history of the personalities and the events, the art and the science of airplane stability and control.

The authors, widely known for their contributions to airplane design and de­velopment, have captured both the technological progress and the excitement of this important facet of aviation. Much of the book’s content captures never-before- available impressions of those active in the field, from pre-Wright brothers air­plane and glider builders straight through to contemporary aircraft designers. The chapters are arranged thematically, dealing with single subjects over their entire history. These include early developments, research centers, the effects of power on stability and control, the discovery of inertial coupling, the challenge of stealth aerodynamics, a look toward the future, and much more. This updated edition includes new developments in propulsion-controlled aircraft, fly-by-wire technol­ogy, redundancy management, applications, and safety. It is profusely illustrated with photographs and figures and includes brief biographies of noted stability and control figures along with a core bibliography. Professionals, students, and aviation enthusiasts alike will appreciate the comprehensive yet readable approach to this history of airplane stability and control.

Malcolm J. Abzug is the former president of ACA Systems.

E. Eugene Larrabee is Professor Emeritus at the Massachusetts Institute of Technology.

Frontispiece George Hartley Bryan (1864-1928). The originator, withW. E. Williams, ofthe equationsofairplane motion. Bryan’s equations are the basis for the analysis of airplane flight dynamics and closed-loop control and forthe design of flight simulators. (From Obit. Notices ofFellows of the Royal Soc., 1932-1935)

The achievements of S. B. Gates, R. R. Gilruth, and others in putting airplane stability and control on a scientific basis have not eliminated a number of early myths attached to the subject. Dr. John C. Gibson (1995) lists no fewer than 15 of these myths and counters them with what we know to be correct. A few of the Gibson’s list of 15 myths and corrections follow:

Wing center of pressure (cp) movement affects longitudinal stability. Correction: Wing cp movement with angle of attack is controlled by the wing’s zero-lift pitching moment coefficient about itsaerodynamic center(1/4 chord), or Cm0. Thisparameteraffectsonly trim for rigid airplanes. Wing cp has been discarded in modern stability and control calculations and replaced by wing aerodynamic center and Cm 0.

A down tail load is required for stability. Correction: Stability is provided by the change in tail load with change in airplane angle of attack. The change is independent of the direction of the initial load.

Gibson comments that this myth survives in FA A private pilot examinations and in an exhibit at the National Air and Space Museum in Washington. This subject is distinct from the instability caused by tail down load in the presence of propeller slipstream, an effect discussed in Chapter 4, Section 6.

A stable airplane is less maneuverable than an unstable one. Correction: Unstable airplanes are notoriously difficult to control precisely. Given light control forces, a sta­ble airplane can be pitched rapidly to a precise load factor or aiming point. Gibson says, “… the [stable] Hurricane, Typhoon, and Tempest were highly manoeuvrable and were greatly superior as gun platforms to the skittish Spitfire.”

The reader is referred to Gibson’s 1995 paper for the rest of these interesting myths and their corrections.

CHAPTER 4

An irreversible power actuator for aerodynamic control surfaces is in principle much simpler than hydraulic control boost. There is no force balancing linkage between the pilot and the hydraulic cylinder to be designed. Irreversible powered controls are classic closed loops in which force or torque is applied until a feedback signal cancels the input signal. They are called irreversible because aerodynamic hinge moments have no effect on their positions.

An easily comprehended irreversible power control unit is that in which the control valve body ishard-mounted to the actuation or power cylinder. Pilot control movement or electrical signals move the control valve stem off center, opening ports to the high pressure, or supply hydraulic fluid and low pressure, or sump hydraulic fluid. Piping delivers high-pressure fluid to one side of the piston and low-pressure fluid to the other. The piston rod is anchored to structure and the power cylinder to the control surface. When the power cylinder moves with respect to structure in response to the unbalanced pressure it carries the control valve

body along with it. This centers the control valve around the displaced stem, stopping the motion. The airplane’s control surface has been carried to a new position, following up the input to the control valve in a closed-loop manner.

The first irreversible power controls are believed to have been used on the Northrop XB-35 and YB-49 flying wing airplanes. Irreversibility was essential for these airplanes because of the large up-floating elevon hinge moment at high angles of attack, as the stall was approached. This was unstable in the sense that pilot aft-yoke motion to increase the angle of attack would suddenly be augmented by the elevon’s own up-deflection. One of the N9M flying scale models of the Northrop flying wings was lost due to elevon up-float (Sears, 1987). The YB-49’s irreversible actuators held the elevons in the precise position called for by pilot yoke position, eliminating up-float. Other early applications of irreversible power controls were to the de Havilland Comet; the English Electric Lightning P1.A, which first flew in 1954; and the AVRO Canada CF-105 Arrow, which first flew in 1958.

Howard (2000) believes that the Comet application of irreversible powered controls was the first to a passenger jet. The U. K. Air Registration Board “made the key decision to accept that a hydraulic piston could not jam in its cylinder, a vital factor necessary to ensure the failure-survivability of parallel multiple-power control connections to single surfaces.”

While irreversible power controls are simple in principle, it was several years before they could be used routinely on airplanes. The high powers and bandwidths associated with irreversible power controls, as compared with earlier boosted controls, led to system limit cycling and instabilities involving support structures and oil compressibility. These problems were encountered and solved in an ad hoc manner by mechanical controls engineer T. A. Feeney for the Northrop flying wings on a ground mockup of the airframe and its control system, called an iron bird. An adequate theory was needed for power control limit cycle instability, to explain the roots of the problem. This was presented by D. T McRuer at a symposium in 1949 and subsequently published (Bureau of Aeronautics, 1953).

The post-World War II history of gradual improvements in the design of irreversible power controls is traced by Robert H. Maskrey and W. J. Thayer (1978). They found that Tinsley in England patented the first two-stage electromechanical valve in 1946. Shortly afterwards, R. E. Bayer, B. A. Johnson, and L. Schmid improved on the Tinsley design with direct mechanical feedback from the second-stage valve output back to the first stage.

Engineers at the MIT Dynamic Analysis and Controls Laboratory added two improve­ments to the two-stage valve. The first was the use in the first stage of a true torque motor instead of a solenoid. The second improvement was electrical feedback of the second-stage valve position. In 1950, W. C. Moog, Jr., developed the first two-stage servovalve using a frictionless first-stage actuator, a flapper or vane. Valve bandwidths of up to 100 cycles per second could be attained. The next significant advance was mechanical force feedback in a two-stage servovalve, pioneered by T. H. Carson, in 1953. The main trends after that were toward redundancy and integration with electrical commands from both the pilot and stability augmentation computers.

In general, satisfactory irreversible power control designs require attention to many details, as described by Glenn (1963). In addition to the limit cycling referred to previously, these include minimum increment of control, position and time lags, surface positioning accuracy, flexibility, springback, hysteresis, and irreversibility in the face of external forces.

Spins are uncontrolled rotations of a fully stalled airplane. In aviation’s early years, when spins were first encountered, spinning airplanes descended more or less straight down. The motion was mainly yawing and quite stable. Stability and control engineers were concerned only with recovery from spins into unstalled flight.

The coming of jet airplanes saw mass distribution changes that caused spins to be oscillatory. Emphasis shifted somewhat to the entry phase of spins and design features that made spin entry less likely during flight operations. This chapter traces the changing nature of airplane spinning from the early days and the corresponding engineering responses.

9.1 Spinning Before 1916

The spinning experience in the early days of aviation is described by B. Melvill Jones (1943):

In the early days of flying – before 1916 – the spin generally ended fatally, because what later proved to be the most effective means of checking it was in some respects contrary to the natural reaction of the pilot to the realization that he was diving towards the earth. About 1916 it was discovered that an effective way of checking the type of spin which was common in those days was to thrust the control stick forward and apply rudder in the sense opposed to the rotation. For some time after this knowledge had become general, relatively few fatalities due to spinning occurred, provided that there was enough air-room for the spin to be checked and the resulting steep dive converted into horizontal flight; the spin then became an ordinary manoeuvre.

Jones goes on to tell of the first flat spins, which occurred around 1919. Previously, spins had been steep in pitch attitude, with corresponding low stalled angles of attack of 25 to 35 degrees. On the other hand, the new flat spins had low pitch attitudes and high angles of attack, 45 degrees or higher, and high rotation rates. The flat spins were more dangerous than the early variety. An interesting speculation is that the invention of the parachute increased the number of survivors who could give reports of spins that had become uncontrollable, thus accounting for a seeming increase in the number of flat spins.

Aerodynamics engineers, including stability and control designers, were baffled in their attempts to get reliable wind-tunnel measurements at transonic speeds, near a Mach number of 1.0. High-speed wind tunnels suffered from the choking phenomenon, in which normal shocks originating on models under test spread across the test section as speed was increased, preventing further increases.

W. Hewitt Phillips credits Robert R. Gilruth with the invention of one method to circum­vent this problem, the wing flow method. Figure 11.6 shows how small wing or complete configuation models are mounted normal to the wing upper surface of an airplane, in a

region where the local Mach number is much higher than the airplane’s flight speed. Phillips describes the method as follows:

A special glove is built on the wing to give a more uniform flow region. As the airplane [P-51 Mustang] goes through its dive and pullout, the model is oscillated back and forth at a frequency of about one cycle per second, to vary either the angle of attack or flap deflection. The forces on the model are continuously recorded with a strain gage balance and a recording oscillograph. The dive lasts about 30 seconds and in this period the Mach number at the model increases from about 0.7 to 1.2… .A vacuum-operated windshield wiper motor was usually used to oscillate the model (Phillips, 1992).

The wing flow method and data from small drop models were both effectively obso- leted with the invention of the porous or slotted-throat transonic wind tunnel by Ray H. Wright, of the NACA Langley laboratory, around 1948. The slotted-throat wind tunnel allows measurements to be made through a Mach number of 1.0.

Informal and rather elementary stability and control derivative extraction took place starting in the early 1950s, when the first electronic analog computers, such as the Reeves Instrument Company’s REAC, were used to get time histories of airplane motions. Numerical values of individual dimensionless stability derivatives, such as C„e, are represented by potentiomenter settings on analog computers. Computed airplane motions appear on pen-type recorder records. The experimenter can try to match an actual flight record for a given control input by resetting potentiometers and rerunning cases over and

over. Since potentiometer settings are controlled by knobs on the face of the analog computer cabinet, this trial-and-error process is known familiarly as knob twisting.

Knob twisting is not altogether a random process, since an experimenter is guided by approximations to the modes of airplane motion. We know, for example, that the period of the Dutch roll oscillation is controlled by the directional stiffness derivative Cn. The amplitude of the roll oscillation relative to that of sideslip or yawing velocity is controlled by the dihedral effect derivative Clp, and so on.

Yaw damping stability augmentation is required for high-altitude airplanes by inescapable physical facts. Dutch roll damping ratio is directly proportional to air density. No airplane can be expected to have satisfactory natural yaw damping at altitudes above about 35,000 feet. So it is also for directional stability at high supersonic speeds, and to a lesser extent for high-altitude pitch damping. Airplanes with stabilizing surfaces compromised or even eliminated for stealth also must have artificial stability or augmentation.

At the other extreme, one sees stability augmentation applied inappropriately, that is, to correct flying qualities deficiencies caused by poor basic aerodynamic design. For example, there is really no reason for static longitudinal stability augmenters to be used in the general – aviation field. This is particularly so when the augmenters are complex, going beyond simple downsprings and adding maintenance and failure problems to be solved.

A case in point is the stability augmentation system used in Piper PA-31T Series Cheyennes. This system is basically a downspring, but with operating speed range and variable spring tension controlled by an angle of attack vane and a computer. A bobweight completes the installation. All this is needed because the basic Cheyenne airframe was derived from a lower powered Piper model, the Navajo. The Cheyenne’s engines are more powerful, but also lighter, leading to aft center of gravity problems. Rebalancing the air­plane would have been a better solution than what we consider to be an inappropriate use of stability augmentation.

The time vector analysis method provides an excellent insight into the modes of airplane motion. The method came about as an incidental result of debugging one of the world’s first electronic analog computers, built to represent generalized airplane longitudinal dynamics. This computer’s inventor was Dr. Robert K. Mueller; his device, now in the MIT Museum, was built to support his 1936 MIT ScD thesis.

The fundamental concept of time vector analysis is that for any oscillatory transient gen­erated by a linear system having a certain undamped natural frequency and damping ratio:

1. the amplitude of the transient derivative is the transient amplitude multiplied by the undamped natural frequency, and

2. the phase of the transient derivative is the phase of the transient advanced by 90 degrees plus the angle whose sine is the damping ratio.

With this concept, one can construct time vector polygons representing each term in any system equation corresponding to a particular modal solution of the characteristic equation. The time vector polygons show which terms are dominant and how the amplitude and phase relations among the variables arise (Figure 18.9). In Mueller’s thesis example, the time vector polygons give insight into the wind axis equations of longitudinal motion and suggest correction of the phugoid mode instability with pitch attitude feedback. At the urging of his then-supervisor at the Glenn L. Martin Company, James S. McDonnell, he presented a paper on the topic at a meeting of the Institute of Aeronautical Sciences (Mueller, 1937).

In Germany, Dr. Karl-H. Doetsch used the time vector method to study lightly damped airplane-autopilot combinations. Working at the Royal Aircraft Establishment (RAE) after World War II, K-H. Doetsch and W. J. G. Pinsker applied time vector analysis methods to the Dutch roll problems of jet airplanes.

There was an early application of the time vector analysis method by Leonard Sternfield of the NACA Langley Laboratory to the Dutch roll oscillation. Around 1951 he built two bridge-table-size mechanical analogs of the roll and yaw time vector polygons to predict the Dutch roll characteristics of new airplanes. Around the same time E. E. Larrabee made what he thought was the first use of time vector analysis to extract stability derivatives from flight time history measurements, although Doetsch had done much the same in England.

The Northrop YB-49 shares with the Boeing B-47 the distinction of being one of the first stability-augmented airplanes in the modern sense (Figure 20.2). Duane T. McRuer (1950) described the YB-49’s yaw damper as follows:

For the sensing part of the system, a Honeywell Autopilot rate gyro was chosen…. An electrical signal is then produced which is proportional to this speed or yaw rate. This signal is fed back through an electrical amplifier and reversible motor. Here the signal is transferred mechanically to a linkage that actuates the rudder cable system. The heavy work, that of opening the clamshell rudder to drag the wing back in line, then falls to the fully-powered rudder hydraulic system.

McRuer since added to this description the information that the reversible motor that put a yaw damping input in series with pilot’s inputs was a turbo-supercharger waste gate servo, as for the B-47. The long cable that runs from the cockpit to the hydraulic servo valves on the clamshell rudders was expected to serve as a backup for the series-installed yaw damper servos. Unfortunately, initial yaw damper actuator motions stretched the cables until the hydraulic servo valve friction was overcome. This created a dead spot until corrected by a reduction in hydraulic valve friction.

McRuer and Richard J. Kulda made the preliminary stability analysis by the method of equivalent stability derivatives, used in the literal approximate factors for the spiral and Dutch roll modes. The detailed design used Bode and Nyquist diagrams, much as in the case of the B-47. The YB-49’s yaw damper had no washout to cancel the yaw rate signal in steady turns. Compared with current practice, the five weeks or so that it took to design, round up parts, install, and check out the YB-49’s yaw damper is of course quite short.