This subject is accorded the recognition of a separate chapter because of the depth of my personal interest in the subject and because of the long period of time over which the problem of spiral instability had repeatedly come up for consideration. In a previous section of this paper, under the heading "Spiral Instability," the tendency of airplanes to diverge from a straight path into a spiral dive was noted. This divergence was said to be so slow that it is rarely noticed by the pilot when he has visual reference to the horizon. If the airplane is flying under instrument conditions, a pilot who is proficient in instrument flight likewise has no difficulty with this type of instability. Many crashes have occurred, however, when novice pilots flew into clouds or fog banks and were unable to keep the airplane flying level. This problem becomes more severe in light airplanes because they are usually equipped just with the basic instrumentation (turn and bank indicator and airspeed) which require considerably more skill to fly blind than an airplane equipped with an artificial horizon.
I was profoundly concerned with this problem because of the experience of one of my professors at MIT The phenomenon of spiral instability and its associated dangers had been discussed by Professor Otto Koppen in his courses on airplane stability and control. He was a pilot himself, and he took me and all his other students up in a Fairchild 24 to give demonstrations of all the stability characteristics discussed in his courses. Shortly after I left MIT, Professor Koppen's sixteen-year-old daughter and her instructor, who was giving her flying lessons, were both killed when their small airplane crashed after flying into a fog bank. Professor Koppen, of course, was devastated and was unable to teach for two years after that.
Development and Tests of the Trim Device
I knew that the problem of spiral instability could be cured with a conventional autopilot, but the existing autopilots were too expensive and heavy to be used in light airplanes. Much of the complication and expense of conventional autopilots resulted from the need to operate the controls in proportion to various signals sensed by instruments in the airplane. This process, in those days, required the use of vacuum-tube amplifiers and complex servomechanisms for converting small electrical signals to mechanical outputs. I therefore gave much thought to a simpler way to perform this function.
I had been interested in bang-bang controls (also called discontinuous controls) in which the signal to operate the control was switched either full on or full off. With this type of mechanism, an on-off contact  replaces the complex electronic amplifier. Such systems can be analyzed by the phase plane method that was described in the book by Minorsky on nonlinear systems (ref. 5.5). Preliminary studies of wing-leveler controls were made by using this technique.
At that time, about 1955, the electronic analog computer had recently become available. This computer greatly aided the study of nonlinear systems. One of the engineers in my branch, Helmut A. Kuenel, set up the problem on an analog computer to study various ideas in more detail than could be done using the phase plane method.
As mentioned previously, most airplanes, whether or not they are inherently spirally stable, will diverge from straight flight because the friction in the control system is large enough to hold the controls deflected from the trim position. To try to overcome this problem, a previous flight study had been made in which preloaded centering springs could be connected to the aileron control linkage to overcome the friction in the system. The spring device could be adjusted to the proper trim position by the pilot. This device prevented the airplane from diverging when it was properly trimmed, but it could not take care of subsequent changes in trim caused by asymmetric fuel usage or by changes in power or airspeed. Evidently, a device was needed to automatically move the centering spring unit to the correct trim position.
A gyroscope was needed to sense yawing velocity (turning) of the airplane and move the centering spring unit as required to cancel this motion. A bang-bang control, in which a slow-moving electric motor connected to the spring unit would be switched to run in one direction or the other, appeared ideal for this purpose. In analytical and analog computer studies, however, the device was shown to need some anticipation of the return of the springs to the trim position, otherwise the device would overshoot the trim position and cause a slow oscillation with the airplane turning first one way and then the other.
Several methods of providing this anticipation (called a lead signal) were tried, all of which were more complicated than desired. Finally, the idea was conceived of simply tilting the spin axis of the gyroscope so that it would sense components of both rolling velocity and yawing velocity. Since the rolling velocity as the airplane rolls into a turn leads the resulting yawing velocity, this method provided the desired lead signal. This method was so much simpler than any of the other techniques that it was immediately adopted.
A suitable gyroscopic device was provided by H. Douglas Garner of the Instrument Research Division. This device, taken from other equipment, already incorporated a pair of contacts on the gyroscope gimbal to provide the desired operation of the trim motor. In addition, it had a means of electrically torquing the gimbal to bias the rate of turn at which the contacts were centered. Mr. Garner later provided valuable ideas on use of this feature in the system. The gyroscope was mounted on a tilting platform and the system was installed in a Cessna 190 airplane available at the NACA Flight Research Division.
The development of the system and results of flight tests are reported in detail in a NACA report (ref. 10.1). A diagram of the system taken from this report is given in figure 10.1. The system provided excellent stabilization of the airplane in smooth or turbulent air. It worked even better than expected as a result of two fortuitous features. First, with the gyroscope set to the correct tilt angle, the airplane, when released from a banked attitude, returned to level flight in a practically deadbeat manner, with little or no overshoot. It would be expected that a different gyroscope tilt angle would be required for each value of airspeed, but it was found (and shown analytically) that the variation of angle of attack of the airplane as it flew at different values of airspeed was in the correct direction, and....
....approximately of the right magnitude, to provide automatically the required variation with airspeed of the tilt angle from the flight path. Second, any bang-bang, or discontinuous, control would be expected to have a small hunting oscillation about the trim position. In the actual installation, however, the engine vibration caused the gyroscope contacts to chatter as the airplane reached the level attitude. As a result, the action of the control approximated a linear control and the hunting oscillation was eliminated. This system then behaved as a "dual mode control" with a discontinuous action at large displacements and a linear action at small displacements. This type of system had been advocated by some control theorists to take advantage of the best features of both types of control, but it had probably never been implemented in such a simple manner.
A problem observed by the pilots was that if the airplane was placed in a steady turn and then manually returned to level flight on a  desired heading, the control system, operating more slowly than the human pilot, would leave the ailerons deflected and would then continue to stabilize the airplane on a heading a few degrees displaced from that desired by the pilot. To avoid this problem, H. Douglas Garner suggested that a pair of force switches be placed on the control wheel between the pilot's grip and the wheel itself, which would apply current to the torquing coils on the gyroscope gimbal. With this system, as the human pilot held the airplane on the desired heading, the airplane would be retrimmed on this heading by the automatic system.
The force switches also allowed the pilot to make constant-rate turns of about three degrees per second for instrument flight maneuvers by holding a small force on the control wheel within the preload of the centering springs. The system therefore provided features of a more sophisticated autopilot in addition to the original objective of acting simply as a wing leveler.
Because of the preload in the centering springs, the human pilot had to apply a control force exceeding this amount (about four pounds on the control wheel) to maneuver or to hold a steady turn. The NACA test pilots objected to this feature because of their experience with airplanes that did not oppose the pilot in holding a banked attitude. Beginners with little piloting experience, on the other hand, generally preferred the feeling that the airplane would return to level flight if the controls were released.
A patent disclosure for the system was filed. At that time, all the NACA patent applications were handled by one man at the NACA Headquarters in Washington. About a year later, the formal NACA report (ref. 10.1 ) was published. I did not know at the time that a formal report placed the invention in the public domain and that the patent application was thereby voided. I was displeased that a year had passed without action by the Headquarters office to file a patent application, but
I did not worry about it because I had no interest in making money from the invention.
Later, when the report became known among light airplane companies and control system manufacturers, about eight of these companies sent representatives to Langley for further discussion of the device. The first question asked usually was, "Is the device covered by a valid patent?" Without a patent to give an exclusive right to produce the device, none of the manufacturers would consider marketing it. As a result, I learned the value of a patent even in cases when the inventor was not interested in making money. Several light plane autopilots were in production at that time and continue to be available today, but because they are expensive and require considerable rebuilding of the airplane for installation, they are rarely used. These problems would have been avoided by the system tested. Mr. Garner has continued research in this field and has produced designs for autopilots suitable for construction and installation by home builders. These devices further extend the capabilities of the device tested by providing a heading hold mode. These devices are highly successful, but unfortunately many light airplanes still are not equipped with autopilots and crashes in instrument flight conditions continue to occur.
The wing-leveler autopilot described is notable because, to my knowledge, it is one of the few successful applications of a discontinuous control system for airplane control. Discontinuous controls have been widely investigated by control theorists. This type of control is theoretically more efficient in correcting for disturbances because it uses the full power of the servomechanism at all times. A control system that uses its maximum effort in correcting for a disturbance that is followed by maximum effort in the other direction to stop the motion at the desired point has been called an optimal bang-bang control, because it can bring the system to the desired point in a shorter time than any other system (for example, a linear system) with the same maximum control  effort. Despite this theoretical advantage, these systems have found little use in aeronautical applications, though they have sometimes been used for spacecraft attitude control. In most cases, the tendency to hunt back and forth in a limit cycle oscillation after correcting for the disturbance has been a serious drawback. The availability of computers makes the study of such systems much easier. In recent years, a group of researchers from a British university came to Langley to discuss their work in this field. They were very surprised to hear that a successful application of a discontinuous control had been made forty years ago.
To conclude this account, the subsequent career of Professor Otto Koppen might be of interest. After the death of his daughter, Koppen eventually went back to teaching at MIT, but his wife made him promise that he would never fly an airplane after that. As long as she was alive, he kept this promise, but after her death he took up flying again. A few years ago, I learned from someone in the Langley Flying Club that Professor Koppen had been observed flying over Langley Field on his way to Florida in an American Yankee, a very small high-performance personal plane. At the time, he must have been in his 80's. Later, I learned that Professor Koppen was the oldest pilot in the country with a full instrument rating and that his plane was equipped with a wing-leveler autopilot and special navigational instrumentation, to the extent that there was no room in the cockpit for anyone but the pilot. He died in 1993 at the age of 96.