Each summer, faculty from universities across the United States travel to Dayton, Ohio to conduct research with faculty from the Air Force Institute of Technology.
“The AFIT Summer Faculty Program provides a great opportunity for faculty and graduate students from civilian universities to collaborate on defense focused research and learn about the extensive collaborations we have with AFRL,” said Dr. Ramana Grandhi, AFIT professor of aerospace engineering. “These partnerships continue even after they return to their campuses.”
During the summers of 2022 and 2023, Dr. Timothy Takahashi, professor of practice in aerospace engineering at Arizona State University, worked with Dr. Grandhi and Dr. José Camberos, AFIT associate professor of aerospace engineering, on hypersonic vehicle flying qualities assessment. Their research collaboration has resulted in the authorship and/or publication of nearly a dozen papers.
"I have been particularly delighted with AFIT's hospitality during my residency on base,” said Takahashi. “In particular, I thank the staff at the D'Azzo Research Library. They have been invaluable in locating papers and reports, which illuminate the development, construction and flight-test of the famous USAF/NASA X-15 hypersonic research aircraft.”
Below is one of the papers that resulted from the summer faculty program.
Hypersonic Vehicle Flying Qualities Assessment for Multidisciplinary Analysis & Design
Dr. Timothy Takahashi, AFIT Summer Faculty, Arizona State University
Dr. José Camberos, Associate Professor of Aerospace Engineering, AFIT
Dr. Ramana Grandhi, Professor of Aerospace Engineering, AFIT
General-purpose hypersonic airframes must demonstrate satisfactory flying qualities over a broad range of speeds and altitudes. Recent collaboration between AFIT faculty, AFRL scientists and academia reexamines lessons learned from the 1950’s and 60’s X plane programs, the Space Shuttle Orbiter, and the X-33 demonstrator.
Abundant X-plane flight test data, archived by the USAF, gathered, and shared with our academic team, (see FIGURE 1), has allowed us to study the successes, failures and close-calls experienced by the X-1, X-2, X-15, XB-70, and various lifting bodies to understand what vehicle design features lead to inherently desirable flying qualities. In order for the next generation of engineers to advance by “standing on the shoulders of giants,” we must identify which design screening methods, first invented during the golden age of X-planes, are most applicable.
FIGURE 1 – The USAF has a long legacy of X-plane concept demonstrators, flown at Edwards AFB.
(X-Planes at Edwards AFB, 1947-1977 Illustration by Mike Machat of from https://flighttestmuseum.org/)
USAF historian Richard Hallion suggests that successful design must involve “the creative integration and exploitation of diverse technologies, including structures, propulsion, aerodynamics and controls.” At the same time, he reminds us to remember George Santayana’s famous dictum: that “those who cannot remember the past are condemned to repeat it.” The USAF has a glorious past where they accomplished the first piloted Mach 1, 3 and 5+ flights (in the Bell X-1, Bell X-2, and North American X-15), albeit not without mishap and loss of life.
Notably, the history of flight dynamics cannot be separated from Dayton, OH. Perkins and Hage wrote their seminal text, “Airplane Performance, Stability and Control,” during their time at Wright Field during the Second World War. They used the draft manuscript to teach officers at the Army Air Forces Engineering School, which is the precursor to today’s AFIT. Their work focused on the practical attributes of applied mathematics; that is the art of using reduced-order mathematical models to design an aircraft to exhibit favorable flying qualities.
Following the War, aircraft speeds increased through the transonic regime, then supersonic to the hypersonic. With each increase, pilots and aircraft began to experience unanticipated instabilities. Sometimes, violent motions about all three axes would suddenly present; the severity of these motions could even result in the loss of the aircraft and pilot. These encounters resulted from strong “coupling dynamics” – unforeseen exchanges in kinetic energy between pitching, rolling and yawing motions characteristic of fast and slender flying machines – driven by otherwise stable inherent motions of the rigid airframe.
Engineers at Edwards AFB first puzzled over these experiences, as common flight-dynamics mathematical approximations preclude their formation. For example, the mathematics behind inertial roll coupling had not been “invented” before 1948 when W.H. Phillips of the NACA first described the possibility of energy exchange between seemingly orthogonal flight dynamics motions. After several X-series research aircraft and Century series fighters encountered severe inertial roll coupling, this work became widely known. R.E. Day, at the NASA High-Speed Research Station - Edwards AFB, further matured these ideas. Discovery of these modes led to the development of new screening methods that proved invaluable to the USAF and its contractors. Phillips’ and Day’s insight led to upsized vertical tails that were essential to making the F-100, F-102 and F-106 aircraft successful; they kept the peace during the height of the cold war. While MIL STD 1797A captures elements of these lessons learned, most recent Aircraft Flight Control books focus more on modern control theory and overlook these practical screening metrics.
A good example of the USAF’s emerging predictive capability involved a hair-raising flight of the Bell X-1A made on December 12, 1953, by the legendary Chuck Yeager. While the X-1A is a three-axis stable aircraft, newly formulated screening criteria predicted sharply degraded controllability above Mach 2, of which Yeager was warned. Shortly after besting the world speed record with level, controlled flight at Mach 2.44, Yeager lost control of his aircraft due to emergent control coupling, as shown by static camera footage in FIGURE 2. The departure was so prolonged and intense that Yeager’s helmet shattered the cockpit canopy. Recovering, after losing nearly 50,000-ft in altitude, Yeager exclaimed “those guys were so right!” While Yeager’s heroic stick-and-rudder skills brought the aircraft to a safe landing, he could easily have died if he had not successfully recovered from that spin.
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FIGURE 2 – Camera Footage from Yeager’s December 12, 1953, X-1A flight. a) Level Flight at M~2.4 with nose slightly elevated and wings level, b) two seconds later, the aircraft has rolled 90o to the right and begun to spin – the camera records only the sky, c) four seconds into the spin, we see the aircraft has rolled 270o and the camera captures the desert floor 75,000-ft below, d) six seconds into the spin we see that the aircraft has inverted (the earth is in the upper frame).
Frame grabs from USAF/NACA sourced flight test camera footage as posted at https://www.youtube.com/watch?v=I7p6f6tPEuU]
Our research team, working from simple, panel-method aerodynamic models of the X-1A can easily generate the aerodynamic data needed to screen for control coupling and inertia coupling behaviors. We use the Bihrle-Weissman plot, developed first by R. Weissman, Chief of the Stability & Control Branch at Wright Laboratory, to rapidly identify regions of the flight envelope where flight maneuvers may be dangerous to execute. Indeed, General Yeager’s near fatal mishap occurred just as he entered the precise area of danger as identified by our modern tools, as shown graphically in FIGURE 3. We note that the X-1A has favorable predicted lateral-directional flying qualities at or below Mach 1.94, at all likely flight attitudes the data is in the Favorable “A” region of the Evolved Bihrle-Weissman plot. Above this speed, we expect controllability to decline precipitously as most flight conditions lie within either region “F” (where flying qualities degrade) or region “B” (where control induced departure is likely).
FIGURE 3 – Revised Bihrle-Weissman Chart for Bell X-1A. The aerodynamic basis to compute LCDP and CnßDynamic as a function of flight speed and attitude was predicted using modern panel-method aero codes.
Our team also assessed the 1963 Neil Armstrong flight in the X-15 which was dramatized in the opening to the 2018 movie “First Man.” On flight 3-4-8, Armstrong inadvertently flew an “atmospheric skip” maneuver where the X-15 glided much further south than planned, see FIGURE 4. We have come to realize that Armstrong’s “atmospheric skip” was the result of overlooked inherent lateral-directional airframe instabilities, which prevented him from properly executing his planned maneuvers, as noted in FIGURE 4. To bleed off speed, the X-15 needed to fly its atmospheric reentry in a turn at a 60-90o bank angle. In this mission, Armstrong’s 4-gee pullup necessitated him to hold a very high angle-of-attack. At that point, the X-15’s Spiral Divergence time constant became unsatisfactory simultaneously with the Dutch-Roll Mode going unstable. This moved its predicted flying qualities from the “A” region on the Bihrle-Weissman plot into the Unstable “U” region. Shortly thereafter, Armstrong “lost control” of bank angle, resulting in the atmospheric skip. He regained control regained control only after crossing over into the Los Angeles basin; sonic booms shook the Rose Bowl. Luckly, Armstrong enough gliding range left to make it back to Edwards AFB without crashing into the San Gabriel Mountains. It should be no surprise that the X-15 program subsequently flew later flights with a revised ventral tail configuration that avoided these problems.
FIGURE 4 – Ground Track of Neil Armstrong’s X-15 Flight 3-4-8 from 1963.
What does this insight mean for future hypersonic systems?
Today, we are blessed with access to modern digital flight control computers that can react faster, and with greater precision, than could any human pilot. These systems will be essential components, integrally designed into any forthcoming Hypersonic aircraft. If we consider a hypersonic aircraft as a cyber-physical system, we must never forget that the physical system imposes finite limits to available bandwidth and control power. Cybernetic control systems, whether classical, modern or AI powered, have only limited ability to command an unruly airframe.
IEEE Fellow Gunter Stein reminds us that “unstable systems are fundamentally, and quantifiably, more difficult to control than stable ones.” Not only that but “closed-loop systems with unstable components are [at best] only locally stable.” Control systems cannot stabilize a fundamentally unstable system if the fundamental instabilities exceed the available bandwidth and/or control power. While modern technology lifts bandwidth limitations arising from sensors and CPU limitations, the powerful servo motors needed to rapidly move control surfaces remain bulky and power hungry. Other bandwidth limitations stem from the airframe itself, as light-weight efficient structures offer greater flexibility than heavier designs. While designers can accurately predict vibrational modes, their frequencies and mode shapes often depend strongly on known variables such as the fuel load. As engineers, we cannot ignore these realities, but must design our systems around these limits.
Modern hypersonic systems, unlike the 1950’s X-planes, will not likely participate in prolonged “envelope expansion” development programs. Modern aircraft are expected to fly well on their first flight. Our team, carefully tailoring methods and metrics first developed at Wright Field and at Edwards AFB can help make this a reality. Our tools, when employed by multi-disciplinary design teams trained in the art and science of aircraft digital engineering, can help “design out” unnecessary flight control risks arising from fundamental aerodynamic characteristics.
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