Category Airplane Stability and Control, Second Edition

The analysis of robust controllers took a different tack from adaptive controls with the work of J. C. Doyle and his associates, starting around 1980. The key to the new approach is a generalization of system gain using the singular values of a matrix. Matrix singular values are another term for the matrix norm, defined as the square root of the sum of the squares of the absolute values of the elements. The matrix norm is the trace of A* A, where A is the given matrix and A* is the Hermitian conjugate of A (or the transpose if A is real).

According to the singular value approach, control system robustness against uncertainties in mechanical and aerodynamic properties is assured if the amplitude of the maximum expected uncertainty is less than the minimum system gain at all frequencies.

A simpler, but equally important application of singular value analysis is to system stabil­ity margins, without considering uncertainties. Stability margins are guaranteed if the mini­mum singular values of the system’s return difference matrix are all positive (Mukhopadhyay and Newsom, 1984). The system return difference matrix I + G is a matrix generalization of the closed-loop transfer function denominator for a single-input single-output system. This stability margin application of singular value analysis was made for the X-29A research airplane (Clarke et al., 1994).

In the late 1980s a counterrevolution of sorts took place, a retreat from authori­tative military flying qualities specifications. A new document (1987), called the Military Standard, Flying Qualities of Piloted Vehicles, MIL-STD-1797 (USAF), merely identifies a format for specified flying qualities. Actual required numbers are filled into blanks through negotiations between the airplane’s designers and the procurement agency. As explained by Charles B. Westbrook, the idea was to let MIL spec users know that “we didn’t have it all nailed down, and that industry must use some judgement in making applications.”

A large handbook accompanies the Military Standard, giving guidance on blank filling and on application of the requirements. The handbook is limited in distribution because its “lessons learned” includes classified combat airplane characteristics. The Military Standard development for flying qualities is associated with Roger H. Hoh of Systems Technology, Inc., and with Westbrook, David J. Moorhouse, and the late Robert J. Woodcock, of Wright Field.

The demise of the authoritative MIL-F-8785 specification was part of a general trend away from rigid military specifications, with the intent of reducing extraneous and detailed management of industry by the government. Industry designers said in effect, “Get off our backs and let us give you a lighter, better, cheaper product” and “Quit asking for tons of reports demonstrating compliance with arcane requirements.” Some horror stories brought out by the industry people did seem to make the point. The Military Standard is in fact ideal for “skunk works” operations; their managers don’t like more than general directions.

However, the Military Standard seems to bring back the bad old days, the “straw man” requirements of the 1930s, established by pilots and engineers based on hunch and specific examples. It is as if the rational Gilruth method had never been invented. A justification of sorts for the counterrevolution is the tremendous flexibility provided stability and control designers with the new breed of digital flight control systems.

Literally, it is now possible to have an airplane with any sort of flying qualities that one can imagine. Tiny side sticks can replace conventional yoke or stick cockpit controls. Right or left stick or yoke controls no longer have to apply rolling moments to the airplane. Instead, bank angle, constant rolling velocity, or even heading change can now be the result. By casting off the bonds of the rigid MIL-F-8785 specification, a procuring agency can take advantage of radical, innovative control schemes proposed by contractors.

The ability of advanced flight control systems to provide any sort of flying qualities that can be imagined brought a cautionary note from W. H. Phillips, as follows:

The laws of nature have been very favorable to the designers of control systems for old – fashioned subsonic, manually-controlled airplanes. These systems have many desirable features that occur so readily that their importance was not realized until new types of electronic control systems were tried.

Don Berry, a senior engineer at the NASA Dryden Research Center, had similar views:

We have systems capable of providing a wide variety of control responses, but we are not sure what responses or modes are desirable.

A further step in the dismantling of “rational” Gilruth flying qualities specifications is the recent appearance of independent assessment boards, charged with managing the flying qualities (and some performance) levels of individual airplanes. Such a board, called the “Independent Assessment Team,” was formed for the Navy’s new T-45A trainer. Team members for the T-45A included the very senior, experienced engineers William Koven, I. Grant Hedrick, Joseph R. Chambers, and Jack E. Linden.

A very early application of plug ailerons was to the Northrop P-61 Black Widow, which went into production in 1943. The P-61 application illustrates the compromises that are needed at times when adapting a device tested in a wind tunnel to an actual airplane. The plug aileron is obviously intended to work only in the up position. However, it turned out not to be possible to have the P-61 plug ailerons come to a dead stop within the wing when retracting them from the up position. The only practical way to gear the P-61 plug ailerons to the cable control system attached to the wheel was by extreme differential. Full up-plug aileron extension on one side results in a slight amount of down-plug aileron angle on the other side. The down-plug aileron actually projects slightly from the bottom surface of the wing. Down-plug aileron angles are shielded from the airstream by a fairing that looks like a bump running spanwise.

Plug-type spoiler ailerons are subject to nonlinearities in the first part of their travel out of the wing. Negative pressures on the wing’s upper surface tend to suck the plugs out, causing control overbalance. Centering springs may be needed. There can be a small range of reversed aileron effectiveness if the flow remains attached to the wing’s upper surface behind the spoiler for small spoiler projections. Nonlinearities at small deflections in the P-61 plug ailerons were swamped out (as an afterthought) by small flap-type ailerons, called guide ailerons, at the wing tips.

Early flight and wind-tunnel tests of spoilers for lateral control disclosed an important design consideration, related to their chordwise location on the wing. Spoilers located about midchord are quite effective in a static sense but have noticeable lags. That is, for a forward-located spoiler, there is no lift or rolling moment change immediately after an abrupt up-spoiler deflection. Since airfoil circulation and lift are fixed by the Kutta trailing – edge condition, the lag is probably related to the time required for the flow perturbation at the forward-located spoiler to reach the wing trailing edge. Spoilers at aft locations, where flap-type ailerons are found, have no lag problems (Choi, Chang, and Ok, 2001).

Another spoiler characteristic was found in early tests that would have great significance when aileron reversal became a problem. Spoiler deflections produce far less wing section pitching moment for a given lift change than ordinary flap-type ailerons. The local section pitching moment produced by ailerons twists the wing in a direction to oppose the lift due

to the aileron. This is why spoilers are so common as lateral controls on high-aspect ratio wing airplanes, as discussed in Chapter 19, “The Elastic Airplane.”

Slot-lip spoiler ailerons are made by hinging the wing structure that forms the upper rear part of the slot on slotted landing flaps. Since a rear wing spar normally is found just ahead of the landing flaps, hinging slot-lip spoilers and installing hydraulic servos to operate them is straightforward. There is a gratifying amplification of slot-lip spoiler effectiveness when landing flaps are lowered. The landing flap slot is opened up when the slot-lip spoiler is deflected up, reducing the flap’s effectiveness on that side only and increasing rolling moment (Figure 5.11).

Airplanes that fly near the speed of sound are designed with thin, stubby wings. Most of their masses are concentrated in the center, in long, slender fuselages. When these airplanes are rolled rapidly the fuselage masses tend to swing away from the direction of flight and become broadside to the wind. This tendency, essentially a gyroscopic effect, is called inertial coupling.

8.1 W. H. Phillips Finds an Anomaly

The distinction of having discovered inertial or roll coupling in airplanes and then explaining it mathematically in the open literature belongs to W. Hewitt Phillips, then working in the Flight Research Division of the NACA Langley Laboratory. In a 1992 paper Phillips said, “When the [XS-1] model was dropped, it was observed in the optical tracker

to be rolling, as shown by flashing of light from the wings____ In examining the records

further the oscillation… was found to represent a violent pitching in angle of attack from the positive to the negative stall” (Figure 8.1).

Phillips analyzed the problem as a gyroscopic effect, publishing his results in an NACA Technical Note (Phillips, 1948). In those days NACA used the category of Technical Notes for “the results of short research investigations and the results of studies of specific detailed problems which form parts of long investigations.” Well, nobody’s perfect – the NACA could hardly be blamed for missing the fundamental importance of Phillips’ inertial coupling results when so many other people took little notice. In hindsight, the inertial coupling analytical work clearly merited publication in the more exalted category of NACA Technical Reports as the “results of fundamental research in aeronautics.”

Until the 1970s, fighter air-to-air combat followed the pattern set during World War I. Fighter pilots maneuver behind opposing fighters to bring fixed guns to bear long enough for a burst. The tactics are much the same for narrow-field-of-view guided missiles, such as the AIM-9 Sidewinder. In the missile case, a tail position is held long enough for an acquisition tone; then the missile is launched.

Hawker-Siddeley in Britain came up with the thrust-vector-controlled Taildog missile concept in the late 1960s, making an off-boresight launch a possibility. Combined with a helmet-mounted sight, a Taildog-type missile can be launched at target airplanes at almost any position where the pilot can follow the target with his eyes. However, even with off – boresight missile lockons and launches now possible, there is still interest in gunnery for air-to-air combat. Furthermore, there is interest in gun bearing at high angles of attack, increasing firing opportunities in a dogfight.

Supermaneuverability is defined as controlled, or partially controlled, flight in the stalled regime. It takes two forms: first, a dynamic maneuver to a high angle of attack, beyond any equilibrium or trim point. Pitching angular momentum carries the airplane to a momentary peak angle of attack. The second form of supermaneuverability is flight to a sustainable trim equilibrium beyond the stall. Supermaneuverability is seen as a way to get into the tail chase position, by a feint, tricking a pursuing airplane into overrunning one’s position. Supermaneuverability adds to a dogfighting airplane’s options.

The Cobra maneuver, demonstrated with a Sukhoi Su-27 airplane by the Russian pilot Viktor Pugatchov at Le Bourget in 1989, is in the first category. After Pugatchov’s demon­stration in the Su-27, the same maneuver was performed in a MiG-29. The Cobra is started from unstalled flight with a rapid application of full nose-up control, which is held up to the maximum angle of attack point, about 90 degrees. Control is neutralized for the recovery, assuming that the airplane has a negative or nose-down pitching moment at that point.

The entire maneuver takes about 5 seconds. There is a small altitude gain but a huge loss in airspeed and kinetic energy. Ordinarily, during air combat, one tries to maximize airspeed and total (potential plus kinetic) energy as a reserve for further maneuvers. Thus, U. S. Major Michael A. Gerzanics, project test pilot for a vectored-thrust F-16, has stated that supermaneuverability is not beneficial in all tactical situations, but is rather something that he would like to have available for close combat with a strong adversary. Clearly, any un­controlled yawing and rolling moments that develop in the 5-second period beyond the stall must be small. The Cobra maneuver has been elaborated with a sidewise variant, called the Hook.

10.2 Unsteady Aerodynamics in the Supermaneuverability Regime

Mathematical modeling in the supermaneuverability regime has to account for unsteady aerodynamic effects above the stall (Zagainov, 1993). Zagainov describes a state variable mathematical model, developed by M. G. Goman and A. N. Khrabrov, for coef­ficients such as Cz and Cm. The model has a first-order state equation that defines time dependence (Figure 10.11). The typical hysteresis loop found in forced oscillation tests into the stalled regime can be modeled in this way. Zagainov also discusses the strong rolling and yawing moments that appear in the angle of attack range where vortices are shed from inboard strakes and extended forebodies. These vortex-generated rolling and yawing mo­ments not only appear to exceed values measured in steady wind-tunnel tests, but they are also time-dependent, exhibiting hysteresis loops.

Additional light on the complex, unsteady air flows in the supermaneuverability regime has been shed by a combined wind-tunnel test and flow visualization program (Ericsson and Byers, 1997). A major factor is a coupling between vehicle motion and asymmetric cross-flow separation on a slender forebody. Wing leading-edge extensions or LEX, such as found on the F-16 and F-18 airplanes, change the nature of the cross-flow separation, apparently in a beneficial direction.

In nearly 100 years of controlled flight the stability and control field has seen any number of special gadgets and phenomena that fit into no general category We recall some of the most interesting of these.

14.1 Fuel Shift and Dynamic Fuel Slosh

The term fuel shift refers to long-term motions of the fuel in a partially filled tank, such as a shift to the rear of an airplane’s tank caused by a prolonged nose-up attitude, in a climb. The causes and effects of fuel shift are apparent. Aft fuel shift could move the airplane’s center of gravity to a dangerously rearward position. This possibility is generally considered by every designer. There is even the possibility of fuel starvation if the tank feeds the airplane’s engine from a forward sump.

Dynamic fuel slosh occurs when fuel in a partially filled tank, be it an automobile or airplane tank, sloshes around inside the tank in response to changing vehicle accelerations. As the tank walls contain the sloshing fuel, transient forces are transmitted to the walls, and the vehicle, by the fuel. Dynamic fuel slosh can be a problem in airplane stability and control if the fuel modes of motion couple with the airplane’s normal modes of motion. The dynamic fuel slosh problem is worth examining because modern jet airplanes tend to have high ratios of fuel to gross weight and slosh motions could have a considerable effect. Also, on airplanes with relatively thin wings, the main tankage tends to be in the fuselage. Wing tanks are generally interrupted by structural members, which act as baffles to fuel motion, while fuselage tanks can have large uninterrupted volumes.

Although dynamic fuel slosh is an intriguing mathematical and engineering problem, documented cases of dynamic fuel slosh coupling with an airplane’s modes of motion are rare. There was a verified case of dynamic fuel slosh coupling with the Dutch roll mode of motion on the Douglas A4D Skyhawk. Partial fuel in a 500-gallon fuselage tank forward of the center of gravity caused undamped roll-yaw oscillations during landing approaches (Figure 14.1). The problem was corrected when fore-and-aft vertical tank baffles were added to the fuselage tank, dividing the tanks into left and right halves. The baffles almost doubled the fuel slosh frequency, decoupling slosh from the Dutch roll.

There was another reported dynamic fuel slosh problem on the Lockheed F-80C airplane. This was during an all-out drive to improve the loitering capability of F-80s in the early months of the Korean War. F-80 units in Korea started carrying unbaffled 265-gallon tip tanks, but soon reported unexplained crashes. At the request of Headquarters, Far East Air Forces, Wright Field flight-tested the 265-gallon tanks on an F-80C.

In a test flight in November 1950, James D. Kelly found no flight problems at takeoff and climb-out, when the wing tip tanks were essentially full. Later, with partial tip tank fuel, an uncontrollable pitching motion started. Kelly could see the wing tips twisting as fuel sloshed fore and aft. He recovered control only after the left tip tank collapsed and fell away and he could jettison the right tank.

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Figure 14.1 Calculated effectof fuselage tank slosh in the Douglas A-4 Skyhawk before installation of a fuselage tank baffle. Fuel motion couples with the Dutch roll mode of motion. With the fuel mass motion limited by the tank sides (dotted curves), a steady limit cycle “snaking” motion results. (From Abzug, Douglas Rept. ES 29551, 1959)

Two additional dynamic fuel slosh cases are known, both documented in U. S. Air Force flight test reports. Both involved fuel slosh coupling with the Dutch roll mode of motion and were excited when the rudder was used to stop the yawing component of the Dutch roll motion. The airplanes with this problem were the Boeing KC-135A and the Cessna T-37A.

An analytical approach to the problem of dynamic fuel slosh coupling with the modes of airplane motion was made possible by a model proposed by Ernest W. Graham (Luskin and Lapin, 1952). Graham used the velocity potential for liquid in a rectangular open-top tank given in Horace Lamb’s classic Hydrodynamics. Sloshing fuel is modeled as a simple pendulum plus a fixed mass below the pendulum. The pendulum angle from the vertical is taken as the average fuel surface angular displacement in its fundamental mode of motion (Figure 14.2). The fuel’s general motion has higher harmonics, of shorter wave lengths, all of which are neglected to define the equivalent pendulum.

The pendulum analogy to dynamic fuel slosh depends mainly on the depth of the fuel in the tank. In the nearly empty case, fuel slosh is simply the wave action in a shallow container. The equivalent pendulum is long, and so is the period of the sloshing motion. In the nearly full or deep tank, the equivalent pendulum is short and so is the slosh period. Graham’s model permitted subsequent analysts to treat the problem of fuel slosh by adding the equivalent pendulum to the equations of airplane motion, as an additional degree of freedom for each partially filled tank.

Albert A. Schy, a skilled NACA analyst, set up the fuel slosh problem without using the Graham pendulum model, by assuming fuel is carried in spherical tanks (Schy, 1952). While spherical tanks are never seen in airplanes, Schy’s model is altogether equivalent to Graham’s model for conventional rectangular or prismatic tanks. Schy’s calculations show significant coupling into the Dutch roll mode of an airplane when the sloshing fuel mass is one-fourth the weight of the airplane.

Dynamic fuel slosh coupling with the longitudinal short – and long-period modes of motion is seldom a problem. There is a slight loss in short-period mode damping, but the long-period or phugoid mode cannot couple measurably with fuel in a partially filled tank unless the fore and aft dimension of the tank is impossibly long (Luskin and Lapin, 1952). Recent dynamic fuel slosh studies on a modern swept-wing jet with long fuel tanks running parallel to the wing spars came up dry, in the sense that slosh in any pair of partially filled tanks had negligible effects on the aircraft’s modes of motion.

In contrast to the modest effects of dynamic fuel slosh (but not long-term fuel shift) for the airplane case, dynamic fuel slosh has been an ongoing concern for large liquid-fueled boost or launch vehicles, such as NASA’s Saturn V Launch vehicle dynamic fuel slosh problems have included coupling with controlled pitch and yaw modes of motion as well as with elastic body bending modes.

Turning to the fuel shift problem in airplanes, an interesting case occurred on the Douglas A4D Skyhawk during early test flights. The A4D’s ultrasimple fuel system has only two

tanks, the fuselage tank, which had sloshing problems before a baffle was installed, and a single integral wing fuel tank, which runs from wing tip to wing tip. The wing ribs provide excellent slosh baffling, but prolonged lateral acceleration can transfer partial wing fuel across the airplane’s centerline.

A4D wing fuel shift shows up as spiral instability, easily corrected by the ailerons (Figure 14.3). However, the early A4D airplanes had a single, or nonredundant, aileron hydraulic

system. When aileron hydraulics malfunctioned at a high Mach number during an early test flight the airplane and pilot James Verdin were lost. The painful lesson was learned. Production A4D (now A-4) airplanes retain the single integral wing fuel tank, but dual, independent aileron power systems now guard against loss in lateral control due to fuel shift.

Another fuel shift incident from the same time period occurred at Wright Field in a North American YF-100 being flown by Captain H. Z. Hopkins. He took off for a short functional check of the 275-gallon external fuel tanks. Only 50 gallons were loaded into each tank; takeoff acceleration shifted this load aft. Fuel was being burned from the forward fuselage tank, adding to the aft shift in cg. The cg apparently shifted aft behind the maneuver point, the point at which pull stick forces are required for positive-load factors. The airplane went through a rapid sequence of positive and negative maneuvers. The external tank fuel somehow shifted forward, and the structurally damaged airplane was brought back under control and landed.

Useful solutions to Bryan’s equations of airplane motion for scientific or engi­neering uses are either roots or eigenvalues or actual time histories, which give airplane responses to specific control or disturbance inputs. Either type of solution was essentially out of the question with the means available in 1911. However, by 1920 Bairstow had found useful approximations that served as starting points for developing eigenvalues from the Bryan equations.

When, later on, research engineers in both the United States and in Britain generated time history solutions to the linearized Bryan equations, it was only with great labor. Early step-by-step numerical solutions were published for the S. E.-5 airplane of World War I fame by F. Workman in 1924. A year later, B. Melvill Jones and A. Trevelyan (1925) published step-by-step solutions for the lateral or asymmetrical motions.

As an advance over step-by-step methods, B. Melvill Jones (1934) applied the for­mal mathematical theory of differential equations to the linearized Bryan equations, pro­ducing a marvelously complete set of time histories for the B. F.2b Bristol Fighter at an altitude of 6,000 feet (Figure 18.5). A generation of pre-electronic-computer engineers struggled through those formal solutions. The complementary function is found first. In addition to using a considerable amount of algebra, one has to find the real and complex roots of a fourth-degree polynomial. The complementary function gives the time histories of the variables of motion under no applied forces and moments, but with arbitrary initial conditions.

The last step in the formal solution is finding a particular integral of the equations. This adds to the complementary function the effects of constant applied moments, such as are produced by deflections of the airplane’s control surfaces. In Jones’ own words, “The numerical computations involved… are heavy, they involve amongst other things, the solution of four simultaneous equations with four variables.” It is little wonder that numerical time history calculations languished for years, until electronic analog computers were commercially available, about the year 1950.

Coupling of the B-47’s yaw damper system with the airplane’s fuselage side­bending mode was resolved simply when the yaw damper’s rate gyro was relocated. That is, the rudder’s yaw damping action cut off at a low enough bandwidth that the side-bending mode itself was not reinforced.

The coupling of stability augmentation systems and airplane elastic modes takes on a new dimension for high-bandwidth control systems. If the flight control system is capable of interacting with the airplane’s structural modes, the stability of the combination must be assured. A conventional approach is gain stabilization, in which control system response at structural mode frequencies is attenuated by notch filters. The notch filters reduce rate gyro and accelerometer outputs in a narrow band around modal frequencies.

While effective, notch filtering invariably introduces lag at lower frequencies, which can adversely affect flying qualities. Phase stabilization (Ashkenas, Magdaleno, and McRuer, 1983) attempts to replace or supplement notch filtering by creating dipoles out of the

structural bending poles. The dipoles are the stable type referred to in the “Transfer Function Dipoles” section of Chapter 20, with the zero below the pole in the s-plane. Zero location for particular modes can be controlled by sensor location, but locations that produce stable dipoles for some modes will be wrong for others.

The insights furnished by the crossover model for compensatory operation lead to criteria that can be used in control system design, as in the Neal-Smith approach. An important example is the Hoh-Mitchell-Ashkenas bandwidth and phase delay criteria (Hoh, 1988), a combination of two individual metrics, illustrated in Figure 21.6.

The first metric is aircraft bandwidth, defined as the frequency at which the phase angle of attitude response to stick force input is -135 degrees. The aircraft bandwidth measures the frequency over which the pilot can control without the need for lead compensation. The second metric is phase delay, defined as the difference in response phase angle at twice the frequency for a -180-degree phase angle and 180 degrees, divided by twice the frequency for a -180-degree phase angle. The phase delay metric approximates the phase character­istics of the effective airplane dynamics, from the region of crossover to that for potential pilot-induced oscillations. Systems with large phase delays are prone to such oscillations.

Boundaries in aircraft bandwidth-phase delay space have been developed using flight and simulator pilot ratings and commentary. Similar boundaries have been especially useful for rotorcraft and special (translatory) modes of control. With these boundaries, designers are able to account for closed-loop pilot-airplane dynamics, using effective airplane dynamics alone. A related airplane-alone criterion based on the crossover model is the Smith-Geddes (1979) criterion frequency. Still another criterion based on airplane-alone dynamics places boundaries in the Nichols plane of the attitude frequency response (Gibson, 1995). The idea is to confine the attitude frequency response within boundaries defined by the best piloted closed-loop flying qualities. All of these boundary methods depend on simple correlation. They should be effective to the extent that new cases resemble those on which the boundaries are based.

Good design practice suggests using all of these criteria to examine airplane dynamics at issue.

Otto Lilienthal (1848-1896), Sir Hiram Maxim (1840-1916), and Dr. Samuel Pierpont Langley (1834-1906) followed the empirical route, much as did the Wrights, but they failed to demonstrate man-carrying mechanical flight mainly because they underesti­mated the problem of control. Lilienthal died of a broken back after losing control of his hang glider. Langley’s airplane flew stably in uncontrolled flight as a quarter-scale model but broke up twice in full-scale launches. Maxim’s steam-driven airplane might have flown, but it broke free of the down-holding rails on its test track and was wrecked.

Maxim’s well-engineered failure has had a continuing fascination for modern aeronau­tical engineers. Bernard Maggin, a noted stability and control engineer with a long career at NACA and the National Research Council, has done extensive research into Maxim’s work for the National Air and Space Museum. Another stability and control expert, W. Hewitt Phillips, built and flew a rubber-powered, dynamically scaled, scale model of Maxim’s large machine. In unpublished correspondence Phillips reports as follows:

The model flies fine, despite the lack of vertical tail on the configuration that Maxim used when he ran it on tracks. It flies like a twin pusher, which is what it is. The big propellers aft of the center of gravity give it a marginal amount of directional stability. …Of course, the Reynolds number is far from the full-scale value, but this may not be very important since Maxim used thin airfoils….

My conclusion is that Maxim’s airplane would have flown, at least as a giant free-flight model…I feel that Maxim should get more credit for his engineering contributions than has been given by historians.

The Wrights, on the other hand, addressed the control problem head-on. They taught themselves to fly with three experimental biplane gliders, each fitted with warpable wings for lateral control and all-moving foreplanes for pitch control. The third incorporated an all-moving vertical tail coupled to the wing warp for suppression of adverse yaw due to lateral control actuation, and they learned to fly it quite nicely by 1902. They applied for a patent, describing coupled lateral, or roll and yaw, controls.

In 1903 the Wrights built a powered machine based on the 1902 glider, with a four – cylinder gasoline engine geared to turn its two propellers, and they designed and built the engine and propellers too. They flew it first on 17 December 1903. Modem analysis by Professor Fred E. C. Culick and Henry R. Jex (1985) has demonstrated that the 1903 Wright Flyer was so unstable as to be almost unmanageable by anyone but the Wrights, who had trained themselves in the 1902 glider. In 1904 and 1905 the Wrights improved the lateral stability of their 1903 airplane by removing the downward arch of the wings as seen from the front (the so-called cathedral), reduced its longitudinal instability by ballasting it to be more nose-heavy, and improved its lateral control by removing the mechanical roll-yaw control interconnect.

Henceforth, appropriate roll-yaw control coupling would be provided by pilot skill. Finally, the Wrights learned to sense wing stall, especially in turning flight, and to avoid it by nosing down slightly. By practice they became masters of precision flight in their unstable machine. They also received a patent for their control innovations on 22 May 1905. Confident of their skill and achievements, they built two new machines and sent one to France in 1907.