Many of the disciplines that I studied in college were useful in my work at Langley, as has been shown in the preceding chapters. Some other subjects of interest, however, were completely new and resulted from the rapid progress of aeronautics during the war years. These topics included compressibility effects, that is, the effect of approach to the speed of sound on the flow around aircraft. The word "compressibility" is derived from the concept that at speeds attained by aircraft prior to WW II, the air flowing over the airplane may usually be considered incompressible because the local changes in pressure or density of the air caused by the passage of the airplane are very small compared to the value of these quantities in the ambient atmosphere. As the airplane flies at a speed approaching the speed of sound, however, these quantities experience changes that are no longer small compared to the ambient conditions. As a result, large changes inflow patterns and aerodynamic characteristics occur.
Another development requiring new approaches was the necessity of hydraulically powered controls in the primary control systems of airplanes. Such systems, as shown previously, were required because the conventional means of operating the control surfaces were ineffective in the transonic and supersonic speed ranges.
Finally, the developments in control theory that occurred during the war allowed studies not only of automatic pilots, but also of the control actions of human pilots in ways that had not been considered previously. Because of the strong dependence of airplane behavior on the actions of the pilot, this subject attracted a lot of attention and became a whole new field of research.
The Wing-Flow Technique
The problem of compressibility effects during dive recoveries of high-speed fighter airplanes during WW II has already been mentioned. In chapter 8 in the section entitled "Roll Coupling," my branch head Robert R. Gilruth was said to have developed two techniques to study compressibility problems, the free-fall method and the wing-flow method. This section describes the wing-flow method and some of the research conducted by this technique. I was not responsible for the invention of this concept. It was typical of Gilruth's approach to research, however, that he did not hesitate to assign capable engineers to work on ideas that he considered important, even though these studies might be quite different from the traditional work of the group. As a result, my section, the Stability and Control Section, was....
....assigned the job of developing the wing-flow technique along with members of the Performance Section, and I was in charge of supervising the design of equipment and conduct of some of the tests.
In the wing-flow method, a small model is mounted on the upper surface of the wing of a fighter airplane. When the airplane dives from a high altitude and a pull out is made at a high but still safe Mach number, the flow on the upper surface of the wing smoothly increases from subsonic to supersonic speeds. A region of reasonably uniform flow exists that may be used as the test region for a small model. The choking phenomenon occurring in closed-throat tunnels does not exist because of the lack of boundaries above and at the sides of the test region.
Figure 11.1 shows a photo of a small model mounted on the wing of a P-51 airplane. A special glove was built on the wing to give a more uniform flow region, and the velocity field in this region was measured in dives before installing the model. As the airplane goes through its dive and pull out, the model is oscillated back and forth at a frequency of about one cycle per second to vary either angle of attack or flap deflection. The forces on the model are continuously recorded with a strain gauge balance and a recording oscillograph. The dive lasts about 30 seconds and in this period the Mach number at the model increases from about 0.7 to 1.2. A drawing of an unswept semispan wing-flow model of a rectangular wing with a full-span flap is shown in figure 11.2, and some of the data obtained are shown in figure 11.3. These results show the ability to study nonlinear aerodynamic characteristics by the wingflow method.
The balances and other equipment for these tests were largely designed by Harold I. Johnson, an engineer in the Stability and Control Section. A vacuum-operated automobile windshield-wiper motor was usually used to oscillate the model or the flap. A single 30-second dive covered the whole range of angle of attack and Mach number, providing as much data as might normally be obtained in a couple of weeks of wind-tunnel testing. As a result, the engineers were soon overwhelmed with data, but they worked....
....hard to evaluate it and to put out reports. As might be imagined, there was considerable criticism of the wing-flow method by some wind-tunnel specialists because of the small size of the models and the nonuniformity of the flow field. Nevertheless, the data obtained provided the only source of information at transonic speeds. Some vindication for the development of the method by the engineers in the Flight Research Division was later received when the wind-tunnel engineers installed a transonic bump on the floor of the Langley 7- by 10-Foot High Speed Tunnel. The flow field over the bump was used to test small models by the same techniques as used for the wing-flow method.
In conventional wind-tunnel testing, the airspeed and model configuration are carefully set to the desired conditions before taking a reading on the balance. In an effort to obtain great accuracy, control surface and flap deflections are sometimes set by building separate inserts for each value of deflection. As a result the tunnel has to be shut down between tests at each control setting, which results in a very long time to complete the tests. To shorten the test time, the number of test points is reduced as much as possible. For example, I have frequently used wind tunnel test data in which readings were taken at increments of five degrees in angle of attack and sideslip and in which control settings or flap settings were limited to a few values through the deflection range. One....
....great advantage revealed by the methods developed for the wing-flow technique was that the data obtained were continuous through the range of variables. As a result, small irregularities or nonlinearities in the aerodynamic forces could be determined with as much accuracy as desired, whereas such features would be missed in conventional wind-tunnel testing. In flight at high speed, the variations of angle of attack and sideslip required to reach the limit loads on the airplane structure are frequently only a few degrees. Any small irregularities or nonlinearities in this range are therefore....
....of extreme importance. The effects of nonlinearities in the variation of rudder hinge moment with angle of sideslip in causing snaking oscillations has already been discussed.
Another desirable feature of the wing-flow technique was that it allowed study of the effect of rate of change of variables as well as the effect of steady values. In actual flight, most flight maneuvers involve changing conditions, but the effects of the rates of change are not studied in conventional wind-tunnel tests.
As a result of these considerations, I and others have made suggestions to wind-tunnel engineers, from time to time, to incorporate provisions in their mounting systems and balances to allow tests under changing conditions. Some progress has been made in use of models with motor-driven control surfaces, but the desire to retain existing equipment and traditional techniques has generally prevented any change in the methods of mounting models or in the use of steady test conditions.
Because of the lack of any other source of transonic data, the results of the wing-flow tests were eagerly sought by the airplane manufacturers during the period following WW II. The tests of the 35-degree swept wing in figure 11.1 showed that the adverse stability and control characteristics at transonic speeds shown by most fighters with unswept wings were avoided by this model. As a result, the Chance Vought Company laid out the design of the F7U Cutlass Navy fighter as a tailless airplane with the same sweep and aspect ratio as the model. Some modifications were later made to incorporate the control surfaces, vertical tails, and fuselage, and a half model of the complete airplane configuration was tested (figure 11.4). The completed airplane is shown under test at the NACA Langley Flight Research Division in figure 11.5. This is probably the only case in history when the design of a new airplane was inspired by data taken in a 30-second test run.
The wing-flow testing continued for some years, but by 1950 Langley aerodynamicists developed the slotted-throat wind tunnel that enabled valid test results to be obtained....
....through the transonic speed range. As a result, testing by the wing-flow and free-fall methods was discontinued.
Power Controls and Pilot-Induced Oscillations
With the development of airplanes capable of transonic and supersonic speeds, the use of manual control systems, even with the use of the accumulated knowledge of closely aerodynamically balanced controls and spring tabs, became impractical. Designers were forced to employ hydraulically actuated controls, even though the pilots and old-time designers were suspicious of the reliability of these devices.
Hydraulically actuated controls actually had a long background of experience, but not in the aeronautical industry. The first hydraulically actuated steering system for automobiles, later called power steering, was invented by a Harvard professor who lived in my home town of Belmont, Massachusetts. He installed the system in a 1923 Pierce Arrow. This system was developed without the aid of the theory of servomechanisms, which did not become available until the 1940's. This inventor did not succeed in convincing the automotive industry to use his invention until WW II, when it was installed in many Army trucks. After this demonstration of its practicality, power steering was soon adopted for automobiles and is now almost universally used.
Hydraulic controls were also used in large Navy gun turrets. These systems had excellent response and accuracy, but were much too heavy for aeronautical use.
The first hydraulic control systems to be installed in airplanes were called power boost controls, which means that a certain fraction of the force to operate the controls was fed back to the control stick so that the control forces would reflect the aerodynamic hinge moments on the control surfaces just as in a manual control system. The first installation of power boost controls was on the ailerons of a Lockheed P-38. The test pilot who made the initial tests of this system said it gave him the feeling of "supreme domination of the air." Evidently the ability  to produce large values of rolling velocity in high-speed flight with light control forces was very desirable.
Installations of power boost controls on large airplanes, however, had less immediate success. These systems installed in the Douglas B- 19, a large four-engine bomber, resulted in a violent pitching oscillation in the landing approach that almost resulted in a crash. Similar systems in the Martin Mars, a large four-engine flying boat, had many development problems.
The first fighter airplane to require power controls was probably the Vought F7U Cutlass. This airplane, a tailless design, required very wide chord elevons, which could not conveniently employ aerodynamic balance. To develop the hydraulic control systems for this airplane, the Vought company installed power controls in an F4U Corsair. This airplane was later made available to the NACA for research work.
This airplane, when flown by NACA test pilots, frequently encountered rather large amplitude, unexpected, longitudinal oscillations when entering turns or pull ups. It was soon realized that these oscillations represented an instability of the combined system consisting of the human pilot, the airplane, and the control system. These oscillations were called pilot-induced oscillations, or PIO for short. After some practice, the pilots could fly without encountering these oscillations, and in fact, found it difficult to reproduce the condition for test purposes. They could, however, detect a tendency for the these conditions to exist. The hydraulic system could be turned off and the airplane flown with manual control, in which case there was no tendency for oscillations.
When the controls were operated on the ground with the hydraulic system turned on, everything felt perfectly normal, just like a stationary automobile with power steering. In this case, however, there was no way for the pilot to judge the response of the airplane. The closed loop involving the airplane, control system, and pilot was broken.
There was much interest in finding the cause of the pilot-induced oscillations and in determining a method to predict such problems on a new airplane before it was flown. I felt that the method used in analyzing the stability of closed-loop systems known as the frequency-response method could be used for this purpose. This method, by this time (about 1950), was available in textbooks. Also, a convenient graphical method called the Nyquist criterion could be used to predict the presence of stability or instability. Some new concepts were used in the application of this method, however. First, from handling qualities experience, control forces rather than control displacements were believed to be the quantity of primary interest to the pilot because the control displacements on the elevator of a fighter airplane at high speed are very small. Second, the concept of considering the human pilot as a black box in a closed-loop system was practically unknown at that time, and reasonable estimates had to be made of a mathematical representation of the pilot's response.
The analysis was made using experimental data on the control system by oscillating the control stick and measuring the resulting control forces and elevator deflections. These tests were made at various values of frequency and amplitude. The normal acceleration of the airplane in response to the elevator motion was determined from well-established airplane stability theory, and the response of the pilot to airplane motion was estimated as a simple transfer function in which the pilot was assumed to apply a control force opposing pitching velocity with a constant time lag of 0.2 seconds. When these results were combined and the Nyquist criterion plotted, conditions of instability were clearly shown. The source of the instability was found to be friction in the hydraulic valve that admitted fluid to the servo cylinder. These valves had tight-fitting rubber seals to prevent leakage of hydraulic fluid and required a force of one to two pounds on the control stick to operate. Further study showed that this valve friction resulted in a.....
...control force almost 180 degrees out of phase with the stick displacement at small amplitudes of motion.
I presented these results at a conference in Washington that was called by the Bureau of Aeronautics of the Navy Department to discuss power control systems. The other conferees were very interested in the data because most previous opinions of the problem had been based on speculation rather than on a rational analysis.
As previously mentioned, there was no indication of any control problem when the control stick was moved with the hydraulic system turned on and the airplane on the ground. A method was desired to demonstrate to the pilots that control difficulties might be encountered in flight. A very rudimentary simulator was built to provide this capability. As shown in figure 11.6, a slide projector was mounted on flexure pivots and driven by a spring attached to the trailing edge of the elevator. The motion was damped by a dashpot consisting of a piston with large clearance moving in a can full of oil. The damping and spring constant could be adjusted so that the response closely approximated the normal acceleration response of the airplane to elevator motion. The projector produced a spot of light on a screen alongside the cockpit with a motion of several inches corresponding to l g change of acceleration. Two lines were drawn on the screen and the pilot attempted to move the light spot rapidly from one line to the other, simulating a 1g pull up. The response with the basic control system could be compared with that with the power control system operating. The response with the power control system on frequently showed an oscillation, which the pilots considered very similar to that obtained in flight.
In the design of modern airplanes, a mock-up of the control system and cockpit controls and instruments is often built to study possible control system problems. This type of simulator, known as an iron bird, can be very useful in studying control feel and response characteristics. Frequently, however, normal acceleration is displayed on a cockpit instrument that has low sensitivity in terms of pointer motion per g units. In flight, the pilot detects changes in acceleration through sensing the force acting on his body. Studies have shown that the sensitivity of the pilot to changes or oscillations in acceleration is very large. To study pilot-induced oscillations, therefore, an instrument with large sensitivity, such as the slide projector device used on the F4U, should be used to give the pilot sufficient stimulus to represent small changes in acceleration.
A test to compare the characteristics of different control systems in flight to determine their susceptibility to pilot-induced oscillations would also be desirable. One technique that was used in the F4U-4B tests is illustrated in figure 11.7. The F4U-4B was flown in close formation with an F9F-3 airplane, which had a manual control system with good control characteristics. First, the records of normal acceleration are shown with the F9F-3 in the lead and the F4U-4B with manual control. Second, the F4U with manual control is leading. In general, the records for the following airplane are expected to show some oscillations as the pilot applies control to maintain a close formation. Third, the F9F-3 is in the lead with the F4U-4B with power control. The large amplitude oscillations of the F4U-4B as the pilot attempts to perform this tight control task are apparent. Finally, the F4U-4B with power control is in the lead. The F4U-4B flight path is somewhat unsteady. The F9F-3 is able to follow these oscillations with a well-damped and rapid type of response. These records show that a task requiring tight control is required to bring out the deficiencies in the control system.
Numerous studies of power controls and feel devices were made by the Flight Research  Division in the early 1950's (ref. 11.1). As aircraft manufacturers gained more experience with power control systems, many of the early problems disappeared as the importance of valve friction was recognized and means to keep the friction low were developed. Pilot-induced oscillations with other causes, however, remain a persistent source of trouble (ref. 11.2). Designers must try to take advantage of accumulated experience and modern analysis and simulation techniques to try to avoid these problems.
Human Response Characteristics
Autopilots for airplanes had been considered by inventors even before the first flight of the Wright brothers. For example, Sir Hiram Maxim in 1893 made a working model of a steam-powered gyroscope and servo cylinder to maintain the longitudinal attitude of an airplane such as his large steam-powered airplane. In 1913 Glenn Curtiss demonstrated hands-off flight with one of his biplanes controlled by an autopilot designed by Elmer Sperry. Later, in the 1930's, Sperry autopilots found practical use in transport airplanes. Anyone working with autopilots could not escape the realization that the human pilot, in controlling an airplane, worked on the same principle as an autopilot. That is, the pilot could sense the disturbances from a desired path and apply corrections through the control system to correct for the disturbances.
In the late 1930's and 1940's, theories became widely available to allow prediction of the controlled motion of an airplane when the action of the autopilot could be stated mathematically by means of a differential equation or by an expression known as a transfer function that related the input and output. With such techniques, the details of the mechanism could be neglected and the device replaced by a black box with the specified transfer function. It was realized that the human pilot could likewise be replaced by a black box if a suitable transfer function for his behavior could be found. Such a formulation would allow prediction of the motion of an airplane under control of a human pilot and might be of value in predicting handling qualities.
Some early attempts at representing the response of a controlled airplane were made by Professor Otto Koppen and his students at MIT. The stability of a controlled airplane was first studied by Koppen in 1935 by assuming that the controls were moved in proportion to the angular deviation of the airplane from the desired attitude (ref. 11.3). Later this work was continued by two MIT students, Herbert K. Weiss (ref. 11.4) and Shih-Nge Lin (ref. 5.7), who took into account lag in the action of the controls. These reports gave very useful information on the action of closed-loop controls, but little attention was given to the question of whether the controls were moved by a human pilot or by an autopilot.
When I started work at Langley, Herbert K. Weiss was working with the Coast Artillery Board at Fort Monroe, also in the city of Hampton, Virginia. He was interested in human control of pointing of guns, or gun laying, as the British called it. We had discussions of the subject, and he described different methods of control application by a human pilot, such as control of position, rate, acceleration, and combinations of these quantities. These ideas were not immediately applicable to airplane control because the only mechanisms for performing these functions were heavy mechanical devices such as differentials and ball-disk integrators. These ideas, however, served to keep up my interest in the subject of human pilot characteristics.
An important advance in the analysis of the human pilot in controlling a dynamic system was made by A. Tustin, a British electrical engineer (ref. 11.5). His problem was to improve the tracking of a moving target by an electrically rotated turret in a tank and controlled by a human operator. He was able to characterize the human operator's response in terms of a simple control law  involving a proportional and a lead term and a constant time lag caused by the combined effects of lags in the pilot's sensory and neuromuscular systems. In addition, he found that the human pilot response contained a superimposed random motion, which he called the remnant. He was able to use the pilot transfer function to determine modifications to the turret control law that would greatly reduce the tracking error. He also suggested methods for further analysis of human pilot response that have occupied researchers for many years since that time.
Inasmuch as military airplanes are used as gun platforms, the tracking accuracy is important in determining the probability of getting hits on the target. Tustin's success in improving the aiming accuracy of tank gun turrets gave hope that similar benefits could be achieved by applying human response theory to airplanes. Also, the handling qualities requirements formulated as a result of the NACA research were all subjective measures, which were based on pilot opinion. The ability to use a mathematical representation of the human pilot gave hope that a more quantitative method of specifying the requirements might be possible. These applications gave an incentive for following closely the results of research in this field.
Early research was generally performed by recording the errors of the human operator in tracking a moving dot on a cathode ray tube and fitting the recorded response with a mathematical function that would match the performance of the human as closely as possible. Work of this kind was performed at MIT and was sponsored by the Wright Air Development Center at Wright-Patterson Field at several research organizations, including Franklin Institute, Systems Technology Incorporated, and the Cornell Aeronautical Laboratory. At Langley, the equipment for conducting such research was not readily available until the development of analog computers and simulators of various kinds. By this time the study of human response had become an extensive field of research with many research organizations taking part. I assigned one of my engineers, James J. Adams, to follow this research and to conduct studies applicable to our interests. This work continued over a period of many years and extended into the period of the space program.
During WW II, the wing loadings of airplanes increased greatly over the values used before the war, and high-lift flaps and large propellers resulted in a very steep glide. In landing these airplanes, pilots customarily kept the power on until just before touchdown to reduce the sinking speed. There was considerable speculation and study, however, on the problems that might be encountered if a power-off landing was required. One of the airplanes most extreme in terms of wing loading and sinking speed was the Martin B-26 bomber. A flight investigation was made on this airplane around 1944 to investigate piloting techniques required. In particular, runs were made in which the pilot glided the airplane toward the ground with successively increasing sinking speed to study the altitude at which the flare should be started and how accurately the pilot could judge the flare when it was started at an altitude much greater than had been used on most previous airplanes (ref. 11.6).
About 1947, I became interested in studying this problem analytically. Previous studies of the landing flare had assumed relatively small values of the glide angle. This assumption allowed the trigonometric terms involving the glide slope to be simplified by the assumptions sin = , cos = 1. This assumption allowed calculation of the flare paths to be made by analytical methods. This assumption was not very accurate with the steep glide angles of the modern airplanes. I felt that flare paths could be calculated quite accurately without this simplification by use of the method of undetermined coefficients referred to previously. In this method, all terms in the equations are expressed as power series in the independent variable t  (time). Coefficients of like powers of t are collected, and the term involving each power of t is multiplied by an undetermined coefficient. In using the method, the lowest order coefficient may be determined from the initial conditions. Then the next higher order coefficient may be determined from this coefficient, and so on until all coefficients have been determined. In the work conducted, terms through the fifth order in t were used. Because the landing flare (in reverse time) is approximately a parabolic curve, the higher order terms rapidly decrease in size and the method is highly accurate.
I set up the method in tables (now called spreadsheets) to be filled in with calculated values by the female computers in the branch. They used mechanical Frieden or Marchant calculators in the work. Many landing flares were calculated for various values of the parameters. It is well-known that the shortest possible landing over an obstacle may be obtained by making a flare at maximum lift coefficient. The starting point of the flare, however, must be at precisely the right point to allow the wheels to touch the ground when the flight path is horizontal. My objective was to study flare paths that would allow a margin for error and to determine how much the landing distance would be increased as a result.
Despite much study, I was unable to determine a satisfactory criterion for the margin of error to be allowed. The error, of course, depends on the ability of the human pilot to judge altitude and sinking speed. Little work had been done on the subject at that time. Also, I came to realize that there were marked differences in the lift and drag characteristics of different airplanes that would affect the results. Airplanes like the B-26 with power off and flaps down would have high drag and a low value of lift-drag ratio throughout the landing maneuver, whereas delta-wing airplanes would have a decreasing lift-drag ratio throughout the flare. As a result, the data were never published. A report with a similar objective was published by Langley engineers Albert E. Von Doenhoff and George W. Jones, Jr. a few years later (ref. 11.7). They used numerical integration in calculating flare paths.
As an aside in connection with the paper by von Doenhoff and Jones, the reader is reminded that von Doenhoff worked in the Low Turbulence Tunnel Branch and was mainly noted for his airfoil studies and for a book by Ira Abbott and von Doenhoff on airfoils. It might be considered surprising that an engineer with this background would undertake a study of airplane landings. This versatility and broad range of interests, however, is typical of many of the leading engineers at Langley during this period. It is this versatility that allowed the engineers at Langley to take a leading role in the space program a few years later, even though this program involved disciplines very different from their former specialties. Von Doenhoff himself made an excellent analysis of space power systems comparing photovoltaic cells and thermoelectric generators (ref. 11.8).
Returning to the subject of landings, flare paths could be determined readily today by integrating the equations of motion on a digital computer. Also, if desired, simulated landings could be made by a human pilot in a simulator with realistic displays of the landing area. Such studies have no doubt been made in connection with the development of more recent airplanes.
One useful result that I did obtain from the study was to show that an airplane such as a delta-wing airplane, which has relatively high lift-drag ratio at low angles of attack and rapidly increasing drag as the angle of attack is increased, could probably be landed quite easily with power off by a human pilot. The flat glide in the approach allows starting the flare at a relatively low altitude. I gave a talk at a department meeting on this subject. This conclusion was confirmed, many years later, when an Air Force pilot safely landed an F-106, a delta-wing interceptor airplane, on the short runway (5000 feet) at Langley after his engine had failed at an altitude of several thousand feet.