Category Airplane Stability and Control, Second Edition

Spinning and Recovery

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.

Transonic Aerodynamic Testing

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

Transonic Aerodynamic Testing

Figure 11.6 A sweptback-wing half-model mounted on the upper wing surface of a North American P-51, for wing flow testing during dives. The model is transonic, while the airplane is not. (From Phillips, Jour, off theAmer. Avia. Histor. Soc., 1992)

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.

14.8.2 Knob Twisting

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.

Modern Canard Tactical Airplanes

The canard disadvantages enumerated above either do not apply or are over­whelmed by other considerations in the case of tactical airplanes designed for superma­neuverability, or for controllable flight beyond the stall. The stability and control of tactical airplanes in the supermaneuverability regime are covered in Chapter 10, “Tactical Airplane Maneuverability.”

Control of the vortex system shed from the fighter nose is known to be critical for controllable flight beyond the stall. Forebody strakes have been found valuable for this purpose. Canards offer another means for shaping the forebody vortex system. They are used in some modern fighter designs, such as the Sukhoi Su-35, the Saab JAS 39 Gripen (Figure 17.3), the IAI Lavi, the Rockwell/MBB X-31A Enhanced Fighter Maneuverability (EFM), and the Eurofighter 2000.

CHAPTER 18

Mean and Structural Axes

Even after the advent of panel methods, there remain controversial aspects of the quasi-static aeroelastic problem, related to the choice of axes. Structural distortions must be referred to some set of reference axes. There are essentially two sets of reference axes that will serve. One choice, called structural axes, corresponds to a natural reference for laboratory structural deflection tests or their analytical equivalent. Structural axes are aligned with a central hard section of the airplane, such as the wing interspar structure at the airplane’s centerline.

The second choice, which is the only one that is consistent with the ordinary pitch – plunge equations of airplane motion, are mean axes. Mean axes are a familiar concept in normal mode analysis. They correspond to the midpoint of normal mode oscillations, the point at which all transverse deflections are momentarily zero. While structural influence coefficients may well be measured or calculated in an arbitrarily chosen structural axis system, pitch and plunge motions of the aeroelastic airplane must be calculated in mean axes, to avoid systematic error (Milne, 1964, 1968). A refinement of mean axes is the use of principal axes in which distributed moments of inertia are accounted for in addition to longitudinal mass distributions.

John H. Wykes and R. E. Lawrence used both mean and structural axes in a 1965 study of aerothermoelastic effects on stability and control, but they noted the difficulties involved in relating airplane angle of attack in the two systems. The angle of attack difficulty found by Wykes and Lawrence is resolved in an offline transformation of the results, such as pitch attitude and angle of attack time histories, from mean to structural axes (Rodden and Love, 1984). The transformation is feasible at the end of the dynamics calculations. The Rodden and Love paper, corrected in Dykman and Rodden (2000), also presents transformation equations from mean to structural axes.

The Rodden papers have an interesting proof of the fallacy of using the more convenient structural axes for dynamics studies in place of mean axes, as has been done by investigators unwilling to face angle of attack difficulties. In a simple swept-forward airplane example using structural axes, load factor and pitching acceleration time histories depend on the fixity choice of the axes, an evidently incorrect result. This error is avoided with mean axes. Mean axes are used in the FLEXSTAB program.

The Crossover Model and Pilot-Induced Oscillations

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.

The Crossover Model and Pilot-Induced Oscillations

Figure 21.4 Pilot-airplane open-loop frequency responses for two configurations of the USAF/ Calspan variable-stability T-33. The upper case, with no pilot-induced oscillations, has the ideal integrator shape in the vicinity of crossover. The lower case, with severe pilot-induced oscillations, has a steeper slope and more phase lag at high frequencies. (From McRuer, STI Technical Rept. 2494-1, 1994)

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.

G. H. Bryan and the Equations of Motion

The mathematical theory of the motion of an airplane in flight, considered as a rigid body with 6 degrees of freedom, was put into essentially its present form by Professor George Hartley Bryan (frontispiece) in England in 1911. In an earlier (1903) collaboration with W. E. Williams, Bryan had developed the longitudinal equations of airplane motion only. Bryan’s important contribution rested on fundamental theories of Sir Isaac Newton (1642-1727) and Leonhard Euler (1707-1783). Today’s stability and control engineers are generally

Figure 1.7 The perturbation form of Bryan’s equations of airplane motion. The longitudinal equations are above, the lateral equations below. Note the absence of control derivatives. (From Bryan, Stability in Aviation, 1911)

astonished when they first see these equations (Bryan, 1911). As his book’s (Bryan, 1911) title indicated, he focused on airplane stability, not control. Aside from minor notational differences, Bryan’s equations are identical to those used in analysis and simulation for the most advanced of today’s aircraft (Figures 1.6 and 1.7).

Not surprisingly, at this early date he does not cover in detail control force and moments, nor does he treat the airplane as an object of control. The perturbation equations in Fig. 1.7 include stability but not control derivatives. The influence of external disturbances such as gusts is also not addressed, although he recognizes this and other problems by presenting a summary of questions not covered in his book that set an agenda for years of research.

Bryan calculated stability derivatives based on the assumption that the force on an airfoil is perpendicular to the airfoil chord. W. Hewitt Phillips points out that while this theory is not the most accurate for subsonic aircraft, it is quite accurate for supersonic aircraft, particularly those with nearly unswept wings, such as the Lockheed F-104. Thus, Bryan might be considered even more ahead of his time than is usually acknowledged.

Bryan obtained solutions for his equations and arrived at correct modes of airplane longitudinal and lateral motion. At the end of Stability in Aviation, Bryan reviews earlier stability and control theories by Captain Ferber, Professor Marcel Brillouin, and MM. Soreau and Lecornu of France; Dr. Hans Reissner of Germany; and Lieutenant Luigi Crocco of Italy.

Little progress was made at first in the application of Bryan’s equations because of the difficultiesof performing the calculationsand the uncertaintiesin estimating the airloadscor – responding to airplane motions. The airloads associated with rolling, pitching, and yawing motions, the so-called rotary loads, were a particular problem. Early efforts were made at the National Physical Laboratory in England to measure these rotary airloads in a wind tunnel.

The evolution of Bryan’s equations of airplane motion into an indispensable tool for stability and control researchers and designers is traced in Chapter 18 of this book.

Special VTOL Jet Inflow Effects

Deflected jet VTOL airplanes such as the Hawker-Siddeley Harrier and the McDonnell Douglas AV-8B Harrier II can have troublesome jet inflow effects on static

Special VTOL Jet Inflow Effects

Figure 4.7 The low tail position that produces good stability at high lift coefficients for swept-wing airplanes can destabilize the airplane as a deflected jet VTOL. The left-hand diagram shows stability with jet power off; the right-hand diagram shows instability for a jet deflection angle of 60 degrees. (Reprinted with permission from SAE Paper No. 864A, © 1964, Society of Automotive Engineers, Inc.)

longitudinal stability. Problems can arise at jet deflection angles that are intermediate between hovering and normal flight.

As shown in Figure 4.7, jet deflection angles of about 60 degrees can put the horizontal tail in an effective high position relative to the jet flow field. This causes large downwash angles over the tail (McKinney, Kuhn, and Reeder, 1964). This occurs in spite of an actual low tail position relative to the wing chord plane, which is necessary on swept wings to avoid transonic pitchup. In other words, finding a single horizontal tail vertical position to give good static longitudinal stability under all flight conditions may be difficult for swept-wing deflected-jet VTOL airplanes of the Harrier type.

An additional inflow problem occurs with tilt-rotor VTOL airplanes at high descent rates at low airspeeds. This problem is shared with rotary-wing aircraft. High descent rates can lead to asymmetric loss in lift and uncontrollable roll, because of upflow through propeller disks due to the descent rate. The upflow interferes with the downflow required for lift.

Downwash and Sidewash

The flow behind wing-body combinations is deflected from the free-stream values, affecting the stabilizing contributions of the tail surfaces. Downwash is the downward deflection of the free stream behind a lifting surface, a momentum change consistent with the lift itself. Sidewash is a sideward deflection of the free stream, related to the side force on the wing-fuselage combination in side-slipping flow. Sidewash at the vertical tail is dominated by vortices that accompany the downwash when sideslip distorts the pattern.

Wing downwash charts for the symmetric flow (no sidewash) case suitable for preliminary design became available in 1939 from Silverstein and Katzoff. Later investigators broadened the design charts to include the effects of landing flap deflection, ground plane interference, wing sweep, and compressibility.

An interesting sidewash effect is the loss in directional stability experienced by receiver aircraft in close trail to tanker aircraft. Following reports of directional wandering of receiver aircraft, Bloy and Lea (1995) tested tanker-receiver model combinations in a low-speed wind tunnel. These results, together with vortex lattice modeling, confirm the loss in receiver directional stability. Rolled-up tanker wing tip vortices acting on the receiver vertical tail in a low position cause the problem.

The Break with the Past

The 1947 NACA tail design requirements for satisfactory spin recovery stood relatively unchallenged until a series of NASA spin tunnel tests and some experiments at the Cessna Company in the late 1970s. Motivated somewhat by the Grumman/American AA-1B Yankee experience, NASA started a broad-based review of light airplane spin re­covery. W. H. Phillips credits Joseph R. Chambers with initiating this work. The centerpiece of the program was a flight test fleet of four airplanes: a Cessna 172 Skyhawk, a modified Beech C23 Sundowner, a nonproduction Piper PA-28R T-tail Arrow, and a modified Yankee. Initial results from the review represent a distinct break with past NACA work, in particular, the 1947 TDPF tail design criterion. Nine tail configurations were tested on a model of the Yankee in the 20-foot Langley Spin Tunnel. Six of the nine designs were predicted to have satisfactory spin recovery characteristics according the 1947 TDPF criterion, yet only four showed satisfactory recovery in the spin tunnel (Burk, Bowman, and White, 1977). The investigators concluded:

On the basis of the results of the present investigation, the tail design criterion for light airplanes, which uses the tail damping factor (TDPF) as a parameter, cannot be used to predict spin recovery characteristics.

According to Burk, Bowman, and White, TDPF was intended to serve only as a conser­vative guideline for tail design, not as a criterion. Having made this decisive break with 30 years of stability and control design practice, the statement is softened somewhat in words that followed those quoted above, as follows:

However, certain principles implicit in the criterion are still valid and should be considered when designing a tail configuration for spin recovery. It is important to provide as much damping to the spin as possible (area under the horizontal tail), and it is especially important to provide as much exposed rudder area at spinning attitudes (unshielded rudder volume coefficient (URVC)) in order to provide a large antispin moment for recovery.

The real thrust of the NASA review of the 1970s lies in the investigation of factors for light-plane spin recovery other than tail design. The NASA and contractor investigators, including H. Paul Stough III, William Bihrle, Jr., James M. Patton, Jr., Steven M. Sliwa, Joseph Chambers, and Billy Barnhart, found that wing and aft fuselage design details affected the results in ways that cannot be ignored. According to John C. Gibson, British spin tests in the 1930s had already disclosed the importance of rear fuselage design.

The evidence on fuselage aft details is not completely clear, because it is bound up in scale effects, or Reynolds number. Side forces, contributing to damping, of square or rectangular fuselage cross-sections appear to be particularly sensitive to Reynolds number. Thus, results from small-scale spin model tests that pin flat, unrecoverable spins to flat-bottomed rear fuselages (Beaurain, 1977) must be considered only tentative. On the other hand, the recent NASA findings on wing design effects on spins are conclusive and important, as detailed in a following section.

Having seen the NASA spin experts make a decisive break with the past, represented by NACA 1946 and 1947 tail design criteria, what advice can one give to designers of new general-aviation airplanes? Well-funded military programs present no problem, since modern spin testing techniques, such as drop models and rotary-balance tests, that are recommended by NASA are available to them. The concern is with light-airplane designers who have been cast adrift, so to speak, with NASA’s abandonment of the TDPF design criteria.

The most reasonable course to take for designers of new light airplanes who have no budget for extensive spin model testing probably is as follows:

1. Follow the 1947 TDPF criteria. The evidence is that the criteria deal with the right design details, even if the numerical values are incorrect in some cases because of the influence of other parameters.

2. Avoid the design details that are implicated in flat, unrecoverable spins: flat – bottomed rear fuselages and wings with full-span leading-edge droop.

3. Design the outer wing panels to be able to accommodate a drooped leading edge, if spin problems appear during flight test.

4. Check with NASA on the possibility of doing spin tunnel, rotary balance, or model drop tests for the new design. NASA is able to consider such tests if the results would be of general scientific interest, covering new ground.