Category Airplane Stability and Control, Second Edition

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.

Airplanes operating from aircraft carriers have stability and control problems not present in land-based airplanes. Some problems arise from the size constraint, to allow airplanes to fit on the elevators of as many carriers as possible. For stability and control engineers this translates into restrictions on tail length, since wings can be folded. Good pilot visibility over the nose is needed for nose-high landing approaches, affecting the airplane’s design at many points. Waveoffs or missed approaches must be made starting from more adverse airspeed and attitude conditions than from field landings. This means positive, safe control near the stall and careful integration with the airplane’s performance design.

Finally, there is the matter of carrier landings. From the moment of starting a final approach to either field or carrier landings an airplane’s path and airspeed must be controlled. Path control is needed to make a touchdown in the correct area, with a reasonable vertical velocity. Airspeed control is needed to keep the touchdown speed within limits. Depending on the on-board avionic equipment, weather conditions, and pilot training and preferences, path and airspeed control for field landings use a variety of visual cues and instrument readings. The important point is that touching down at a precise point is seldom required for field or airport runway landings.

In contrast to the airport runway case, touchdown point precision to within a very few feet is necessary for successful landings on aircraft carriers. Carrier landings are made without flare. Thus, low approach speeds are desirable to reduce touchdown vertical velocity and landing gear loads. There is little tolerance for errors in touchdown airspeed between stalling and excessive speed, leading to hard landings. As a result, carrier landing accidents, mainly due to hard landings and undershoots, are statistically more common than airport landing accidents.

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.

It is not at all certain that the supersonic Concorde will be followed by fleets of new supersonic cruise civil transports. However, the prospect of subsonic commercial jet transports larger and heavier than the Boeing 747-400 is almost a certainty, with some Airbus A380 superjumbo jets already on order. Thus, it is reasonable to review the expected stability and control problems for very large airplanes.

23.1 The Effect of Higher Wing Loadings

Higher wing loadings than on airplanes of the Boeing 747-400 and advanced 777 classes seem inevitable for commercial airplanes of the 1,000-seat category, if these air­planes are to fit into current airport terminals, runways, taxiways, and maintenance facilities that have had reasonable modifications. Folding wings, tandem main wings, or some other radical departures from current technology would get around the necessity of higher wing loadings, but radical innovations are unlikely in airplanes that will be as expensive as super­jumbo jets. All-wing superjumbo jets have been studied by several groups, but the Boeing and Airbus designs for superjumbo jets show quite conventional arrangements.

Some of the stability and control consequences of using high wing loadings in very large airplanes can be predicted. Higher wing loadings than current practice imply higher fuel weights relative to the aerodynamic forces generated by the wings and stabilizing surfaces. Dynamic fuel slosh effects, a nonproblem for 747-class airplanes, will require a fresh analytical look.

As mentioned earlier, the German air forces in World War II operated under a set of military flying qualities requirements related to the Gilruth set of 1943. The growth of civil aviation after the war led to a number of national and world-wide efforts to specify flying qualities requirements, in order to rationalize aircraft design and procurement in each country and the international licensing of civil aircraft. The goal of internationally agreed upon civil aircraft flying qualities standards is the responsibility of the International Civil Aviation Organization (ICAO), an arm of the United Nations. Annex 8 of the ICAO Standardsdealswith airworthiness, which includesadequate flying qualities(Stinton, 1996).

Standards have also been adopted by individual countries for both civil and military machines. An earlier section traced the evolution of U. S. flying qualities specifications for military aircraft. Similar evolutions took place all over the world. British military specifi­cations are in the UK DEF STAN publications. In particular, DEF-STAN 00-970, issued in 1983, is similar in style to MIL-F-8785C and provides much the same information (Cook, 1997).

British civil flying qualities requirements were embodied initially in the BCARs, or British Civil Airworthiness Requirements. European standards now apply, as found in the European Joint Aviation Requirements, or JARs, issued by the Joint Aviation Adminis­tration. The U. S. versions are the Federal Air Regulations, or FARs, parts 21, 23, 25, and 103 of which deal with airplanes. The wording of the stability and control airworthiness requirements of the FARs is similar to the Gilruth requirements of 1943, which were also concerned with minimum rather than optimum requirements.

Experimental or wind-tunnel studies of rapidly opening upper-wing surface spoil­ers show a momentary increase in lift, followed by a rapid decrease to a steady-state value that is lower than the initial value. At a wind speed of 39 feet per second, the initial increase is over in less than a half-second, and steady-state conditions appear in about 3 seconds (Yeung, Xu, and Gu, 1997). Results from the computational fluid dynamics method known as the discrete vortex method also predict the momentary increase in lift and associate it with a vortex shed from the spoiler upper edge in a direction that increases net airfoil circulation in the lifting direction. A subsequent shed vortex from the wing trailing edge in the opposite direction reduces circulation to the steady-state value. While suggestive, experimental flow visualization results do not exist that confirm this vortex model.

The Yeung, Xu, and Gu experiments show that providing small clearances between the spoiler lower edge and the wing upper surface reduces the momentary increase in lift following spoiler extension. This is consistent with a small shed vortex from the spoiler lower edge of opposite rotation to the vortex shed at the upper edge. A clearance between spoiler and wing surface of this type has also been used to reduce buffet.

The B-52’s elevator is as narrow in chord as is the rudder. It depends on help from an adjustable stabilizer for long-term trim and airspeed changes. As in the case of the vertical tail, the original Boeing design called for an all-moving horizontal tail, but this was abandoned because of doubts as to hydraulic actuator reliability.

The B-52’sadjustable stabilizer isdriven by two independent hydraulic motorsthrough an irreversible screw jack mechanism. One motor drives the jackscrew and the other the live nut on the driven screw thread (Figure 7.6). The control valve for each hydraulic motor is worked

either by an electric motor or by a backup cable drive from the cockpit. The electric motors are controlled in turn by the usual push-button arrangement on the pilot’s control yoke.

With all of this redundancy, stabilizer adjustment failures can still occur, but the B-52 is landable in an emergency with elevator control alone, regardless of stabilizer position. Some center of gravity adjustment by fuel pumping is necessary for this to work.

Time domain response specifications get around the need for equivalent systems. A standard time domain response form was used in the 1987 version of the U. S. flying

qualities standard, MIL-STD-1797 (Figure 10.8). Other time domain response criteria have been proposed, as follows:

The C* Parameter L. G. Malcolm and H. N. Tobie originated the C* parameter, to blend normal acceleration and pitch rate responses to pitch control input. C* is actually a weighted, linear combination of the two responses, akin to the weighted performance indices used in optimization calculations.

The Time Response Parameter Some years later, C. R. Abrams enlarged on the C* parameter approach with a time response parameter that includes time delay in addition to the earlier normal acceleration and pitch rate terms.

Gibson Dropback Criterion This refers to the pitch attitude change following a commanded positive pulse in airplane angle of attack. Pitch attitude increases during the pulse. A pitch attitude decrease after the pulse ends is called a drop – back. A slight dropback is associated with fine tracking. A large or negative dropback (pitch overshoot) creates unsatisfactory pitch short-period behavior.

Special Time Response Boundaries Upper and lower boundaries for longitudi­nal response was a still later specification form, used widely for landing approach responses in addition to up-and-away flying. The space shuttle Orbiter’s longitu­dinal control response is governed by such boundaries (Figure 10.9), apparently established in simulation.

Gibson (2000) comments that the upper boundary in particular severely limits rapid acquisition of angle of attack change in response to pitch demand and was responsible for space shuttle touchdown problems. He says further:

The UK HOTOL project (a horizontal take off Shuttle equivalent) was studied at Warton.. .By designing to optimum piloted pitch response dynamics, i. e., with a rapid flight path response and hence considerable pitch rate overshoot, accurate automatic touch­down was easily achieved in simulation.

Further progress in understanding and improving longitudinal maneuverability has made use of closed-loop studies using the human pilot model (see Chapter 21).