Category Airplane Stability and Control, Second Edition

The algorithmic or linear optimal control model is partially a structural pilot model in that elements of the optimal controller can be identified with the neuromuscular lag. However, the basic distinction between the algorithmic and structural pilot models is that, except for simple problems, the pilot cannot be represented with a simple transfer function in the algorithmic case. When very simple airplane dynamics (a pure integrator) are postulated in order to be able to generate a pilot transfer function, the linear optimal control pilot

model is found to be of high order, but with characteristics similar to the crossover model (Thompson and McRuer, 1988).

The linear optimal pilot model hasbeen used to advantage in the generation of pilot ratings (Hess, 1976; Anderson and Schmidt, 1987), the analysis of multiaxis problems (McRuer and Schmidt, 1990), and the stability of the pilot-airplane combination in maneuvers (Stengel and Broussard, 1978).

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.

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.

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 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

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.

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.

A literal approximation to a mode of airplane motion is defined as an approximate factor that is a combination of stability derivatives and flight parameters such as velocity or air density. This approximation is quite distinct from the factors that are obtained from the airplane’s fourth – or higher degree characteristic equations, factors that are necessarily in numerical form. Literal approximations to the modes have a long history, starting with Lanchester in 1908. A feedback systems analysis approach to developing and validating approximate modes was developed by Ashkenas and McRuer (1958).

A well-known and usually quite accurate literal approximation to the roll mode is for the roll mode time constant TR. The roll mode time constant is the time required for rolling velocity to rise to 63 percent of its steady value following an abrupt aileron displacement. The approximation is TR = -1 /Lp. The symbol Lp = Clpq Sb2/(2 VIx), where

Clp = dimensionless roll damping derivative, a function of wing planform para­meters such as aspect ratio and sweep angle; q = flight dynamic pressure, (p/2) V2;

S = wing area;

b = wing span;

V = flight velocity;

p = air density;

Ix = roll moment of inertia.

Note that all of the individual parameters in the roll mode approximation would nor­mally be known to an airplane designer. A large literature has been produced on literal approximations to the modes. McRuer (1973) lists four reasons for this interest, as follows:

1. Developing the insight required for the determination of airframe/automatic – control combinations that offer possible improvements on overall system complexity.

2. Assessing the effects of configuration changes on aircraft response and on air – frame/autopilot/pilot system characteristics.

3. Showing the detailed effects of particular stability derivatives (and their estimated accuracies) on the poles and zeros and hence on aircraft and air – frame/autopilot/pilot characteristics.

4. Obtaining stability derivatives from flight test data.

To this list one might add that mode approximations provide a reasonableness check on complete solutions generated within massive digital-computer programs, assuring that no input errors have been made. Literal approximations to the modes are obtainable only if the equations of motion themselves are simplified in some way, or if the factorization itself is approximated.

Mode approximations are useful in the ways McRuer lists as long as the approximations are simple ones, easy to grasp. One can improve the approximations, bringing the numerical values closer to the actual factors of the characteristic equation. This can provide additional insight into aircraft flight mechanics. However, if the literal expressions are lengthy, their utility suffers. The improvement to the classical Lanchester result for the phugoid mode period made by Regan (1993) and others (see Chapter 11, Sec. 13), which adds only one simple term but greatly improves accuracy at high airspeeds, is an example of a useful improved approximation, in the context of McRuer’s comments.

On the other hand, the improved modal approximations of Kamesh (1999) and Phillips (2000), while demonstrating considerable mathematical skills and adding to our under­standing of flight dynamics, are probably too complex for the applications mentioned by McRuer.

The first stability augmenters appeared during World War II. Little detailed in­formation is available about them. A German Blohm and Voss Bv 222 flying boat was thought to have had a pitch damper acting through a small, separate elevator surface. In a paper delivered in 1947, M. B. Morgan described an experimental yaw damper installed on a Gloster Meteor jet airplane. Other notable early designs were the Boeing B-47 and the Northrop YB-49 yaw dampers and the Northrop F-89 sideslip stability augmenter, which are discussed below.

20.5.1 The Boeing B-47 Yaw Damper

The B-47 Stratojet was a radical airplane in its time, a six-jet bomber with very flexible sweptback wings. Early flight tests disclosed that damping in yaw at low airspeeds was much less than pilots could deal with in landing approaches. The main pilot objection was to the rolling portion of the motion, caused by the dihedral effect of the swept wings at high angles of attack. After discarding other alternatives, Boeing engineers decided to attack the rolling motion indirectly, by artificial yaw damping using a rate gyro and the airplane’s rudder. That is, by suppressing side-slipping motions, the airplane’s rolling moment due to sideslip would not cause the objectionable wallowing in landing approaches.

The engineers who were chiefly responsible for the XB-47 yaw damper design were William H. Cook and Edward Pfafman. Roland J. White, who made a frequency-response analysis of the XB-47 yaw damper design, provides a complete account of the development (White, 1950). In White’s account one can find all of the elements that go into modern stability augmenter designs, even though in unfamiliar form in some cases. These are

the application of servomechanism analysis, using the equations of airplane motion;

airframe mathematical model includes aeroelastic bending effects; irreversible power controls;

stability augmentation series servo, isolating the pilot from the servo action; artificial feel system.

Roland White’s XB-47 yaw damper servomechanism analysis, using inverse frequency response, was advanced for its time. However, the all-important matter of loop gain, or commanded rudder angle per unit yaw rate, was apparently settled in flight test. William Cook remembers that Robert Robbins, the XB-47 test pilot, had a rheostat that varied yaw damper gain, and that Robbins chose the value that seemed to work best.

With no fund of stability augmenter design information to draw upon, Cook and Pfafman improvised the yaw damper both in terms of design requirements and hardware. A short phone call from Cook at the Moses Lake flight test site to Pfafman laid out the key design requirements of rudder damping authority (one-fourth of full travel) and series actuation. The yaw damper servo was an electric motor and amplifier that had been used for B-29 turbo-supercharger waste gate control (Figure 20.1).

White’s paper was delivered at the Design Session of the Institute of the Aeronautical Sciences 1949 Annual Summer Meeting in Los Angeles. The concept of stability augmen­tation as a normal design feature for swept-wing airplanes had not yet been established, and White’s paper irritated at least one purist. According to Duane McRuer, this person, a respected professor of design at Cal Tech, got off the following comment during the paper’s discussion period:

If the B-47 had been designed properly, it would not have needed electronic stability augmentation.

William H. Cook (1991) reports a similar reaction from an MIT professor, unhappy that an “artificial” solution had been used on the B-47 to solve an aerodynamic stability problem. Of course, there is a perfectly sound aerodynamic reason why yaw stability augmentation is needed on jet airplanes and is not an evidence of poor design. Approximately, Dutch roll damping ratio is directly proportional to atmospheric density. An airplane with a satisfactory damping ratio of 0.3 at sea level will have a damping ratio of only 0.06 at an altitude of 45,000 feet.

The designers of the B-2 stealth bomber proved that the stability and control requirements for a subsonic-level bomber can be met without vertical tails. What is not clear is whether the more severe fighter stability and control requirements can be met without vertical tails.

All designs in a USAF Wright Laboratory multirole fighter study have either small ver­tical tails or none at all (Figure 22.4) (Oliveri, 1994). The preferred replacement for normal vertical tails is thrust vectoring and split ailerons. These controls were used successfully on the NASA/Boeing X-36 Fighter Agility Research Aircraft. A 28-percent-scale remotely piloted model was flown in 1997, reaching an angle of attack of 40 degrees.

A thrust vectoring scheme used to replace fighter vertical tails must have a high – bandwidth actuator responding to sideslip signals for directional stability as well as other stability-augmentation system signals and commands from the pilot. Unless split ailerons are used, for safety reasons it would seem necessary for a thrust vectoring sideslip loop to provide directional stability even at idle thrust. Alternately, engine thrust could be di­verted left and right when idle thrust is needed and modulated for directional stability and control.

All in all, stability and control engineers should come well prepared at design meetings where stealth is the topic.

Airplane stability and control theory in the modern sense began with Frederick William Lanchester. Lanchester was not really a theoretician but a mechanical engineer who devoted most of his effort to the construction of very innovative motor cars. He performed aeronautical experiments with free-flying gliders. He speculated correctly on the vortex theory of lift and the nature of the vortex wake of a finite wing but was unable to give these ideas a useful mathematical form. His free-flying gliders were inherently stable and exhibited an undulating flight path, which he analyzed correctly in 1897. He misnamed the motion the “phugoid,” intending to call it the “flying” motion; actually he called it the “fleeing” motion, having forgotten that the Greek root already existed in the English word “fugitive.”

Lanchester published two books, Aerodynamics in 1907 and Aerodonetics in 1908, which expressed his views and the results of his experiments. He even talked with Wilbur Wright, evidently to no avail, because Wilbur had no understanding of inherent stability in flight, already demonstrated by Penaud, Langley, and Lanchester on a small scale.