: The use of mathematical models of the human pilot in analyses of the pilot/vehicle system has brought a new dimension to the engineering treatment of flying qualities, stability and control, pilot/vehicle integration, and display system considerations. As an introduction to such models, elementary concepts and specific physical examples are used to set the stage for a step-by-step development of what is known about the human pilot as a dynamic control component. In the process, quasi-linear models for single-loop systems with visual stimuli and multiloop systems with visual stimuli are presented and then extended to cover multiloop, multi-modality situtations. Empirical connections between the pilot dynamics and pilot ratings are also considered. Some of the most important nonlinear features of human pilot behavior in adapting to changes in the character of the stimuli are described and tied to the quasi-linear models.

https://apps.dtic.mil/dtic/tr/fulltext/u2/775905.pdf

Mathematical Models of Human Pilot Behavior

Introduction I N 1961, Howard London presented a paper at the 29th Annual Meeting of the Institute of the Aeronautical Sciences in which he demonstated the possibility of using aerodynamic forces to produce an orbital plane change with an expenditure of energy significantly smaller than that associated with an extra-atmospheric propulsive maneuver. Since that time, numerous studies of aeroassisted orbit transfer have been carried out for a wide variety of Earthorbital and planetary missions. Almost any mission that involves changes in orbital altitude and/or inclination in the vicinity of an atmosphere-bearing planet is a candidate for aeroassist. For ease of discussion these many possible mission applications may be categorized as 1) synergetic plane change, 2) planetary mission applications, and 3) orbital transfer vehicle applications. The term, synergetic plane change, is commonly used to denote a maneuver in which a change in orbit inclination is accomplished through a combination of aerodynamic and propulsive forces rather than through propulsion alone. While the maneuver is applicable to any planet with a suitable atmosphere, practically all studies to date have dealt with low Earth orbit missions. As illustrated in Fig. 1, a retrorocket burn causes the vehicle to leave its initial low Earth orbit (LEO) and dip into the atmosphere. During the atmospheric pass, the vehicle is banked so that the lift vector is in a lateral direction, thus producing an aerodynamic turn. As will be discussed subsequently, this turn is often accomplished with continuous thrusting sufficient to balance the aerodynamic drag. Following the aerodynamic turn, the vehicle is reboosted to the desired orbital altitude and a rocket burn is effected to circularize the orbit (shown by the dashed low Earth orbit in Fig. 1). The typical orbital transfer vehicle (OTV) maneuver is in many ways similar to the synergetic plane change. In the OTV case, however, the vehicle is initially in a high Earth orbit (HEO)—geosynchronous in most studies—and must undergo a sizeable velocity decrement in its transfer to LEO as illustrated in Fig. 1. This velocity decrement is more efficiently achieved through a combination of aerodynamic drag and propulsion than through propulsion alone. The OTV mission usually involves some change in orbital plane—for instance, the return from geosynchronous orbit to a typical Shuttle orbit involves a plane change of 28.5 deg. If the OTV is a lifting configuration, some of the required plane change can be achieved by banking the vehicle as in the synergetic plane change maneuver. In planetary mission applications, aeroassist is again used to produce a velocity decrement through aerodynamic drag. For these missions two distinctly different applications of aeroassist have been studied: 1) aerocapture in which the velocity decrement achieved in a single deep atmospheric pass is sufficient to transfer the vehicle from its hyperbolic approach trajectory to a target orbit about the planet (i.e., the vehicle is captured by the planet's gravitational field); and 2) multipass aerobraking in which the vehicle is transferred from its approach trajectory to a highly elliptic orbit about the planet by a rocket burn and then the orbit is circularized by many high-altitude atmospheric passes, each followed by small corrective rocket burns at apoapsis to maintain the periapsis altitude low enough to produce the desired drag decrement but high enough to avoid excessive aerodynamic heating. The first type of planetary application, as illustrated in Fig. 1, is similar to the OTV maneuver except that it usually has a larger velocity excess and no plane change. The second type of planetary application is illustrated in Fig. 2. As is also illustrated in Fig. 2, this type of multipass orbit lowering has also been studied for the GEO-to-LEO OTV mission. In the intervening years since London presented his paper in 1961, many studies have been carried out and a rich literature has developed. In the process of researching the present paper, an extensive bibliography was compiled. It lists the relevant publications in chronological order for each of the three vehicle classes considered. While certainly incomplete (new and additional references keep turning up), this collection of papers is believed to present an accurate overall picture of the evolution of aeroassist technology. Examination of this bibliography shows that the various aeroassist mission applications received their most intensive study in different time periods. As was mentioned previously, the serious study of synergetic plane change maneuvers began with London's paper in 1961. Actually, there were studies published prior to 1961 (e.g., Ref. 1) but London's paper appears to be the first to convincingly demonstrate a significant performance gain. During the 1960s, synergetic plane change was studied extensively with the peak activity occurring around 1967. The initial

A Survey of Aeroassisted Orbit Transfer

Synopsis: From the nostalgic remembrance of the first dynamic flight test this Survey Paper traces several milestones in the history of flight vehicle system identification. A comprehensive account of modern system identification techniques is provided. Several challenging examples bring out the fact that these techniques have reached a high level of maturity, making them a sophisticated and powerful tool not only for research purposes, but also to support the needs of the aircraft industry. This survey paper includes 183 references and provides a consolidated list of publications on the subject.

https://dlr.de/ft/en/portaldata/2/resources/dokumente/ft/jategaonkar/evol_sysid.pdf

Evolution of flight vehicle system identification

The acceleration guidance concept is to plan an aerodynamic acceleration proe le that integrates to the desired e nal position and velocity and satise es all vehicleconstraints and to track theacceleration proe le. The longitudinal entryguidanceforthespaceshuttleisaccelerationguidance;adragdecelerationproe lethatintegratestothedesired downrange and satise es the vehicle constraints is planned and tracked primarily by bank-angle adjustments. The kinematics relating the drag proe le to the downrange assume that the entry trajectory is a great circle arc. In this paper we consider lateral as well as longitudinal motion in acceleration planning. Three differential equations that are the kinematic relations between the aerodynamic accelerations and the position and velocity variables with energy as the independent variable are used as the basis for two methods of planning the drag and lateral acceleration proe les. The e rst is simpler and produces a feasible trajectory for a given angle-of-attack proe le. The second requires more computation, but produces an optimal trajectory using both angle-of-attack and angleof-bank variations to control the entry trajectory and has greater capability to shape the entry trajectory. Both methods are demonstrated using an X-33 vehicle model. The optimal method is capable of achieving a specie ed e nal heading angle and adjusting the number of bank reversals.

Reduced-Order Entry Trajectory Planning for Acceleration Guidance

The practical application of parameter estimation methodology to the problem of estimating aircraft stability and control derivatives from flight test data is examined. The primary purpose of the document is to present a comprehensive and unified picture of the entire parameter estimation process and its integration into a flight test program. The document concentrates on the output-error method to provide a focus for detailed examination and to allow us to give specific examples of situations that have arisen. The document first derives the aircraft equations of motion in a form suitable for application to estimation of stability and control derivatives. It then discusses the issues that arise in adapting the equations to the limitations of analysis programs, using a specific program for an example. The roles and issues relating to mass distribution data, preflight predictions, maneuver design, flight scheduling, instrumentation sensors, data acquisition systems, and data processing are then addressed. Finally, the document discusses evaluation and the use of the analysis results.

Application of parameter estimation to aircraft stability and control: The output-error approach

measured acceleration D/W, gr's drag coefficient lift coefficient drag, force along the total velocity vector ( Ib local gravitational acceleration, ft/sec altitude, distance along radial axis, ft constant feedback control gain lift, force normal to the total velocity vector (<7z,$/ 2)PVVb distance from planet center, ft surface area upon which force coefficients are based, ft differential operator notation time circumferential velocity normal to radius vector, fps dimensionless ratio u/(circular orbital velocity), u/ (gr) total velocity, fps vertical velocity along radial axis, fps weight of vehicle, Ib downrange, distance to destination along great circle route, ft vehicle angle of attack atmosphere density decay parameter, ft ~~ variation in quantity from that of nominal trajectory flight-path angle, positive for climb influence function time-varying feedback control gain atmosphere density, slugs /ft* vehicle roll angle heading angle between the instantaneous great circle route and the great circle route to the target damping factor = natural frequency final value initial value : respect to nominal trajectory

Survey of atmosphere re-entry guidance and control methods

This paper traces the evolution of the use of state estimation in the analysis of aircraft flight data and discusses some recent applications associated with airline turbulence upsets and high-angle-of-attack flight tests. A unifying mathematical framework for state estimation is reviewed, and several examples are shown that illustrate a general approach for estimating variables that are difficult to measure. It is hoped that the diversity of the applications discussed and the examples presented will make the flight-data analyst mindful of the potential advantages of using state estimation methods.

Applications of state estimation in aircraft flight-data analysis

Digital flight records from reported clear-air turbulence incidents are used to determine winds and turbulence, to determine maneuver g loads, and to analyze control problems Many cases of severe turbulence are found downwind of mountains and thunderstorms where sharp, sudden jolts are associated with vortices in atmospheric waves Other cases of severe turbulence are round in strong updrafts above thunderstorm buildups that may be undetected by onboard weather radar An important finding is that there are large maneuvering loads in over half of the reported clear-air turbulence incidents Maneuvering loads are determined through an analysis of the short-term variations in elevator deflection and aircraft pitch angle For altitude control in mountain waves the results indicate that small pitch angle changes with proper timing are sufficient to counter variations in vertical wind For airspeed control in strong mountain waves, however, there is neither the available thrust nor the quickness in engine response necessary to counter the large variations in winds

Severe turbulence and maneuvering from airline flight records

This paper briefly describes a practical technique for obtaining weighted least-squares estimates of aircraft attitude angles, positions, and velocities from measurements recorded during routine flight tests. The measured accelerations and attitude rates are used as inputs to six-degree-of-freedom kinematic equations. Unknown parameters such as measurement biases and initial conditions are determined using a quasi-lineariz ation identification method. This technique has been successfully used in a variety of flight test situations and with several types of aircraft. Particular results include trajectory smoothing during the transition and hover of V/STOL aircraft and the measurement of turbulence during the flight of a probe aircraft through the vortex wake of a large jet transport. Other types of results, briefly noted, include the estimation of instrument calibration terms, the determination of winds, the estimation of states not originally measured, arid the determination of aerodynamic derivatives.

Quasi-Linearizatioh Technique for Estimating Aircraft States from Flight Data

Advanced analysis methods, applied to airline digital flight records and air traffic control radar tracking data, are providing new insight into atmospheric disturbances that cause serious operating problems for aircraft. Reviewed in this paper are performance-based methods for determining unmeasured flow angles and the possible influence of rain on lift and drag, and a state estimation procedure for determining winds along the flight path. The methods are applied to data records from the Delta Airlines flight 191 windshear accident at the Dallas-Ft. Worth Airport, Aug. 2, 1985, involving an L-1011 airliner on final approach. The results indicate that the aircraft encountered a strong downflow that exceeded 40ft/s along with a headwind-to-tailwind change that exceeded 100 ft/s. The outflow near the ground was accompanied by large, rapid changes in vertical wind, consistent with the presence of imbedded vortices. Although rain was present in the "downburst," the analysis showed no evidence of rain causing a loss in aircraft performance.

Rodney C. Wingrove

Papers

Survey of atmosphere re-entry guidance and control methods

Applications of state estimation in aircraft flight-data analysis

Severe turbulence and maneuvering from airline flight records

Quasi-Linearizatioh Technique for Estimating Aircraft States from Flight Data

Analysis of windshear from airline flight data