Category Airplane Stability and Control, Second Edition

Control Sensitivity and Overshoots in Rapid Pullups

When powerful, light longitudinal controls became available for tactical airplanes, the problems of oversensitivity, sluggishness, normal acceleration overshoots, and pilot – induced oscillations appeared. Airplane-pilot coupling, also called pilot-induced oscilla­tions, is properly dealt with as the combination of the dynamics of human pilots with that of their airplanes (see Chapter 21). However, oversensitivity, sluggishness, and overshoots may be understood in simpler terms, that of the airplane alone, without specifically in­volving pilot dynamics. A fundamental indicator of airplane-alone pitch response is the pitch rate transfer function for elevator or stabilizer control inputs (Figure 10.2). Under the usual constant-airspeed assumption, this function has a second-order denominator and a first-order numerator. Although a pure delay may be added, only three parameters are involved: the frequency and damping ratio of the second-order term and the time constant of the first-order term. A number of criteria on oversensitivity, sluggishness, and overshoots deal with this airplane-alone transfer function.

10.3.1 Equivalent Systems Methods

Equivalent systems or low-order approaches refer to fitting an airplane-alone transfer function to the complex dynamics of actual airplane and flight control systems. Hodgkinson, La Manna, and Hyde (1976) are generally referenced as the origin of the

Control Sensitivity and Overshoots in Rapid Pullups Control Sensitivity and Overshoots in Rapid Pullups

A mechanism or complete system with input x and output y defined by the differential equation

can be represented by the transfer function in the Laplace variable s:

Y(s) _ K(sn + a1sn 1 + ••• + an-1s + an)

X(s) = sm+n + b1sm+n-1 + ••• + bm+n_ 1s + bm+n ^

An example is the pitch rate transfer function for elevator or stabilizer inputs, with the airspeed degree of freedom suppressed:

q(s) _ (Ms + ZsMw)s + ZsMw — MsZw

S(s) = s2 —(UoMw + Zw + Mq)s + MqZw — UoMw •

In these equations, a, b = constants K = gain

Ms, Zw, etc. = control and stability derivatives q = pitching velocity s = Laplace variable Uo = forward speed S = elevator or stabilizer deflection.

Figure 10.2 The transferfunction concept. (Adapted from AircraftDynamics andAutomatic Control, by McRuer, Ashkenas, and Graham, Princeton U. Press, 1973)

equivalent systems method. The McRuer, Ashkenas, and Graham approximate factors, with time delay added from variable stability NT-33 tests carried out by Dante DiFranco, were used to match frequency responses of the Neal-Smith data set.

Transfer function criteria, for the airplane alone or the equivalent system, have the authority of a great deal of analysis, simulator, and flight research. Excellent reviews of this field are given by Gibson (1995) and by Hoh and Mitchell (1996). While the original work on transfer-function-based criteria was concerned with tactical airplanes, these criteria were used as well in the flight control designs of modern transport airplanes such as the Boeing 777 (Ward, 1996) and the Airbus series, starting with the A320.

Commercial and Kit-Built Ultralight Airplanes

There are three classes of commercial and kit-built ultralight airplanes, each with interesting stability and control characteristics. Using the terminology of the influential Jane ’sAll the World’s Aircraft, the most simple is the classical modern hang glider, developed from the Rogallo wing (Rogallo et al., 1960). Control is obtained by shifting body weight, as in the nineteenth-century Lilienthal hang gliders. The next level of sophistication is called a parawing. It is a powered ram air parachute. Finally, there is the broad category of microlights. These airplanes range from powered hang gliders to lightly constructed airplanes of conventional layout. Like the hang glider, microlights use fabric-covered light structures.

The FAA in the United States and the CAA in the United Kingdom have each de­veloped certification provisions for ultralight airplanes, FAR Part 103 (1990) and BCAR Section S-CAP 482, respectively. FAR Part 103 applies to unpowered ultralights weigh­ing less than 155 pounds and powered ultralights weighing less than 254 pounds; powered ultralights have top speeds less than 55 knots and stalling speeds less than 24 knots. Part 103 specifically exempts these ultralights from meeting airworthiness standards. Operating rules only are specified. Other countries use the FAA and CAA standards for their own certifications.

A comprehensive review of hang-glider stability and control is presented by Anderson and Ormiston (1994). Longitudinal trim is provided by reflexed airfoil shapes. Directional stability is generally positive because of wing sweep. Geometric dihedral is adjusted for neutral spiral stability at cruise. A surprising finding is low Dutch roll stability at low angles of attack. This has led to pilot-induced oscillations, augmented by inadvertent swing of the body in response to side accelerations. Hang-glider full-scale tests on an outdoor mobile test rig were conducted at Cranfield University (Cook and Kilkenny, 1987).

The stability and control characteristics of powered hang gliders, called flexwing air­planes by the author, were discussed by Brooks (1998). Turn control of these machines is unconventional, as in the case of the Gossamer Condor. To turn right, the pilot’s weight is moved to the right by exerting force to the left on the control frame base bar. The weight moment and aeroelastic wing flexing (right wing washout) combine to start a right roll. Adverse yaw causes right sideslip. Anhedral, or negative dihedral effect, increases the right rolling moment, accelerating the turn.

Commercial and Kit-Built Ultralight Airplanes

Figure 13.1 Chinook WT-11 ultralight airplane, general arrangement. (From Roderick, 1986)

A brief wind-tunnel test of the fabric-covered wing and tail surfaces of a Chinook WT-11 ultralight airplane (Figure 13.1) conducted in the Canadian NAE 9m by 9m low-speed wind tunnel (Roderick, 1986) showed some unusual characteristics. There was noticeable wing twist at higher dynamic pressures, which decreased wing lift curve slope. With the elevator deflected, the horizontal tail had nonlinear lift curves near its stall. The investigators concluded that a large amplitude pitch down at the stall was a possibility.

Aside from the technical findings of these investigators, experience has shown that inad­vertent stalling is a major cause of ultralight accidents. Operators of ultralights under U. S. FAR Part 103 are not required to pass knowledge or experience tests. However, avoidance of inadvertent stalling during the demanding operations of approach and landing requires careful training.

The F-111 Aardvark, or TFX

Practical variable sweepback came along just in time for the all-service TFX concept, which later became the Air Force’s F-111 (Figure 16.1). The F-111 uses the

The F-111 Aardvark, or TFX

Figure 16.1 The F-111 with wings fully swept at 72.5 degrees and fully unswept at 16 degrees.

(USAF photos)

The F-111 Aardvark, or TFX

retractable glove vane reduces excessive longitudinal stability with the wings fully swept back. (From Loftin, NASA SP 468, 1985)

Alford-Polhamus-Wallis rotation-only mechanism. The wing sweep range is 16 to 72.5 degrees, with normal subsonic cruise at a sweep of 26 degrees. Triply redundant three-axis stability augmentation is used. There are no particular stability and control problems with this machine.

The Elastic Airplane

Aeroelasticity deals with the interactions of aerodynamic and inertial forces and aircraft structural stiffness. Additional significant interactions with aerodynamic heating and automatic control systems give rise to the Germanic-length terms aerothermoe – lasticity and aeroservoelasticity. Aeroelasticity concerns stability and control, dealt with here, but also flutter and structural loads arising from maneuvers and atmospheric turbu­lence. Aeroelasticity affects airplane stability and control in a number of areas. Prediction of aerodynamic data at the design stage (Chapter 6), tactical airplane maneuverability (Chapter 10), the equations of motion (Chapter 18), and stability augmentation (Chapter 20) are all affected.

Aeroelastic effects are considered as distractions by many stability and control engineers, obscure problems that get in the way of the real work at hand. Aeroelastic methods are certainly abstract, involving such arcana as normal modes. How does one fix body axes in a flexible structure? What is its angle of attack? We trace this difficult but important branch of stability and control from the early days of Samuel Langley, the Wright brothers, and Anthony Fokker to the present.

The early days were dominated by isolated occurrences of aeroelastic problems and ad hoc solutions. The advent of large-scale digital computers and finite-element or panel methods for the first time provides, if not a general theory, at least an organized approach to prediction and solution of stability and control aeroelastic problems.

Practical Problems with Digital Systems

When digital stability-augmentation systems first appeared, their most alluring advantage, as compared with analog systems, was their ability to change system gains, shaping networks and even architecture by software changes, instead of requiring time­consuming hardware changes. This is especially attractive in a prototype flight testing program, as may be imagined. However, a drawback to this capability is that the ease of making changes by software modifications encourages a cut and try approach to fixing problems.

The same design freedom that makes for easy changes in a digital stability-augmentation system makes it easy to load the design with overly complex gain schedules and cross-feeds. In a recent classified program, practically all system gains are complex functions of altitude, Mach number, angle of attack, center of gravity, and other measurable parameters, with no real proof that this complexity is needed. One result of complex gain schedules is an inordinate amount of time required for checkout in simulation and flight testing.

On the hardware side, one can be faced with digital flight control systems that incorporate several sampling systems, operating at different rates and not in synchronization. This is the case on the Grumman X-29A digital flight control system. Again, careful simulation and bench testing is needed to be sure that no problems arise from this. Anti-aliasing filters are generally needed on the inputs of analog-to-digital converters, to screen out input frequencies that are multiples of the digital sampling frequency.

Changing Military Missions and Flying Qualities Requirements

Flying qualities requirements for general aviation and civil transport airplanes are predictable in that these airplanes are almost always used as envisioned by their designers. This is not so for military airplanes. The record is full of cases in which unanticipated uses or missions changed flying qualities requirements. Four examples follow.

A4D-1 Skyhawk. The A4D-1, later the A-4, was designed around one large atomic bomb, which was to be carried on the centerline. A really small airplane, the A4D-1 sits high on its landing gear to make room for its A-bomb. The airplane was designed to be carrier-based. However, the A4D-1 was used instead mainly as a U. S. Marine close-support airplane, carrying conventional weapons and operating from single-runway airstrips, often in crosswinds. The vestigial high landing gear meant that crosswinds created large rolling moments about the point of contact of the downwind main tire and the ground. In simpler terms, side winds tried to roll the airplane over while it was landing or taking off. Originally, pilots reported that it was impossible to hold the upwind wing down in crosswinds, even with full ailerons. Upper surface wing spoilers had to be added to the airplane to augment aileron control on the ground.

B-47 Stratojet. This airplane started life as a high-altitude horizontal bomber. Its very flexible wings were adequate for that mission, but not for its later low-altitude penetration and loft bombing missions. Loft bombing requires pullups and rolls at high speed and low altitude. In aileron reversal ailerons act as tabs, applying torsional moments to twist a wing in the direction to produce rolling moments that overpower the rolling moments of the aileron itself. This phenomenon limited the B-47’s allowable airspeed at low altitudes.

F-4 Phantom. The F-4 was developed originally for the U. S. Navy as a long-range attack airplane, then as a missile-carrying interceptor. A second crew member was added for the latter role, to serve as a radar operator. Good high angle of attack stability and control were not required for these missions, but then the U. S. Air Force pressed the F-4 into service in Vietnam as an air superiority fighter. Belatedly, leading-edge slats were added for better high angle of attack stability and control.

NC-130B Hercules. This was a prototype C-130 STOL version, fitted with boundary layer control. The airplane’s external wing tanks were replaced by Allison YJ56-A-6 turbo­jets to supply bleed air for the boundary layer control system. At the reduced operating air­speeds made possible by boundary layer control the C-130’s unaugmented lateral-directional dynamics, or Dutch roll oscillations, were degraded to unacceptable levels.

“Systems engineering” as a discipline was a popular catchphrase in the 1950s. Airplanes and all their accessories and logistics were to be developed to work together as integrated systems, for very specific missions. The well-known designer of naval airplanes Edward H. Heinemann was not impressed. Heinemann’s rebuttal to systems engineering was, “If I build a good airplane, the Navy will find a use for it.” Heinemann’s reaction to systems engineering seems justified by the four cases cited above, in which flying qualities requirements for the airplanes changed well after the designs had been fixed.

Hydraulic Control Boost

Control boost by hydraulic power refers to the arrangement that divides aerody­namic hinge moment in some proportion between the pilot and a hydraulic cylinder. A schematic for an NACA experimental boosted elevator for the Boeing B-29 airplane shows the simple manner in which control force is divided between the pilot and the hydraulic boost mechanism (Figure 5.16). Boosted controls were historically the first hydraulic power assistance application.

Hydraulic Control Boost

Figure 5.16 A very early hydraulic-boost control, installed by NACA for test on a Boeing B-29 elevator. Boost ratio l/d is varied by adjusting the location of point A. (From Mathews, Talmage, and Whitten, NACA Rept. 1076, 1952)

By retaining some aerodynamic hinge moments for the pilot to work against two things are accomplished. First, the control feel of an unaugmented airplane is still there. The pilot can feel in the normal way the effects of high airspeeds and any buffet forces. Second, no artificial feel systems are needed, avoiding the weight and complexity of another flight subsystem. Hydraulic power boost came into the picture only at the very end of World War II, on the late version Lockheed P-38J Lightning, and only on that airplane’s ailerons. After that, hydraulic power boost was the favored control system arrangement for large and fast airplanes, such as the 70-ton Martin XPB2M-1 Mars flying boat, the Boeing 307 Stratoliner, and the Lockheed Constellation series transports, until irreversible power controls took their place.

5.13 Early Hydraulic Boost Problems

Early hydraulic boosted controls were notoriously unreliable, prone to leakage and outright failures. Among other innovative systems at the time, the Douglas DC-4E prototype airplane had hydraulic power boost. Experience with that system was bad enough to encourage Douglas engineers to face up to pure aerodynamic balance and linked tabs for the production versions of the airplane, the DC-4 or C-54 Skymaster.

A similar sequence took place at the Curtiss-Wright plant in St. Louis, where the Curtiss C-46 Commando was designed. At a gross weight of45,000 pounds, the C-46 exceeded O. R. Dunn’s rule of thumb of30,000 pounds for the maximum weight of a transport with leading – edge aerodynamic balance only. Thus, the CW-20, a C-46 prototype, was fitted initially with hydraulic boost having a 3:1 ratio, like those on the Douglas DC-4E Skymaster prototype and the Lockheed Constellation. However, maintenance and outright failure problems on the C-46’s hydraulic boost were so severe that the Air Materiel Command decreed that the airplane be redesigned to have aerodynamically balanced control surfaces. The previous successful use of aerodynamic balance on the 62,000-pound gross weight Douglas C-54 motivated the Air Corps decree. This was the start of the “C-46 Boost Elimination Program,” which kept one of this book’s authors (Larrabee) busy during World War II.

Another airplane with early hydraulically boosted controls was the Boeing 307 Strato- liner. Hydraulic servos were installed on both elevator and rudder controls. Partial jamming of an elevator servo occurred on a TWA Stratoliner. This was traced to deformation of the groove into which the piston’s O ring was seated. The airplane was landed safely.

Inertial Coupling and Future General-Aviation Aircraft

Inertial coupling has been generally tamed as a potential problem in modern fighter aircraft. Even the most austere of these are equipped with stability augmentation systems that can provide the required feedbacks to minimize excursions in rapid rolls. The McDonnell Douglas F/A-18A is typical in having feedbacks that minimize kinematic coupling in rolls. This means that when the pilot applies roll control, pitch and yaw control are fed in to make the airplane roll about the velocity vector rather than about the longitudinal axis. Thus, angle of attack is not converted into sideslip angle, reducing sideslip in rolls at high angles of attack.

But what about future general-aviation aircraft? The answer is that the problem could conceivably be rediscovered by general-aviation designers the hard way a few years from now, as it was stumbled upon by fighter designers in the early 1950s, some years after the basic theory had already been developed by W. H. Phillips.

There have been a few fighter-type general-aviation designs already, such as the Bede Jet Corporation’s BD-10 and the Chichester-Miles Leopard four-seat jet. The BD-10 is a two-seat kit airplane that weighs 4,400 pounds and uses an engine with a thrust of nearly 3,000 pounds. The flight control system is entirely manual, with no provisions for stability augmentation.

The BD-10 has the classic inertial coupling-prone design: small, thin wings and a long, heavily loaded fuselage. We have only to imagine the advent in a few years of inexpensive, reliable, jet engines in the BD-10’s thrust class, or even smaller. If this happens, designers will certainly produce fast, agile, personal jet aircraft that would be ripe for inertial coupling problems.

CHAPTER 9

P-51 and P-39 Dive Difficulties

North American P-51 Mustang compressibility dive tests were made at Wright Field in July 1944 in response to fighter pilot reports from combat theaters. Captains Emil L. Sorenson and Wallace A. Lien and Major Fred Borsodi were the pilots in these tests (Chilstrom and Leary, 1993). The P-51 was climbed to an altitude of 35,000 feet, then power-dived to reach Mach numbers where compressibility effects on stability and control were found. Using a newly developed Mach number meter, the onset was found to be at a Mach number of 0.75. The tests were carried out to a Mach number of 0.83.

Longitudinal trim changes and heavy stick forces were encountered, but for the P-51 Mach number increases beyond 0.83 were limited by heavy buffeting. So many rivets were shaken loose from the structure that the airplane was declared unsafe, and the tests were concluded. It was on this series of dive tests that Major Borsodi saw the normal shock wave as a shimmering line of light and shadow extending spanwise from the root on the upper

surface of the wing. Skeptics were silenced only when photos taken by a gun sight camera on later flights showed the same thing.

The Bell P-39 Airacobra was dive tested a few years later at the NACA Ames Laboratory L. A. Clousing was the pilot, a flyer who had a strong interest in stability and control theory. The P-39 had a fairly thick wing; the NACA 0015 at the root, tapering to the NACA 23009 at the tip. Nose-down trim changes and increased stability were encountered in dives up to a Mach number of 0.78. Compressibility effects were a bit obscured by fabric distortion on the airplane’s elevator.

Flight Vehicle System Identification from Flight Test

There are 21 stability and control derivatives that are fairly important in the equa­tions of airplane motion. Model testing in wind tunnels provides good measurements of the important derivatives, values that serve the practical purposes of preliminary stud­ies and control system design. Stability derivative predictions from drawings do almost as well.

In spite of these well-established sources, there has been a long-time fascination with the idea of extracting stability and control derivatives as well as nonlinear and unsteady effects from flight test data on full-scale airplanes or large flying models. One argument is that automatic control system design would be on a firmer basis if it dealt with equations of motion using actual flight-measured aerodynamic forces and moments.

14.8.1 Early Attempts at Identification

Of the 21 important derivatives, one and one only can be extracted in flight tests with simple measurements and with a high degree of accuracy. This is the longitudinal control derivative Cms. Longitudinal control surface angles to trim at various airspeeds at two different center of gravity locations provide the necessary data for this extraction, the aerodynamic pitching moment balanced by a well-defined weight moment. This procedure was used to measure Cms on cargo gliders.

Obtaining Cms using a weight moment inevitably led to somewhat ill-considered plans and even attempts to do the same for the lateral and directional control derivatives. The lateral case would require dropping ballast from one wing; the directional case would require dropping wing ballast while the airplane is diving straight down.