Specification of operational flight profiles and dynamics - CiteSeerX

Specification of operational flight profiles and dynamics: a structured approach Neale L. Fulton Mathematical and Information Sciences Commonwealth Scientific and Industrial Research Organisation (CSIRO) Canberra, ACT 2601, Australia [email protected], Fax: 06 216 7111 Abstract Commercial-off-the-shelf flight simulators are now reconfigurable through user interface software and have a significant increase in the number of parameterised aerodynamic co-efficients available to model the fidelity of flight performance. This leads to more stringent requirements concerning the management and interpretation of flight performance data which in turn means that certification of safety critical functionality of advanced avionics, inclusive of flight simulators for training purposes, is increasingly more complex to manage. A structured approach to management and traceability of aerodynamic data is required, along with quantitative measures of simulation fidelity which can relate flight test data, simulation model detail and sensitivity analyses of avionics functional performance. The principles of the approach presented in this paper are well known in aerodynamics literature and apply to all classically designed aircraft. However the consistent and structured application of these principles in flight simulator standards has not been well presented and needs to be re-addressed with the advent and ready availability of the user reconfigurable flight simulator. The approach presented brings advantages of greater management visibility to simulation needs, and the potential for a controlled hierarchy of inter-related suite of models relevant to the life support of one aircraft type. Practical application of this approach has allowed for a more a straight-forward definition of flight dynamic requirements and a check on completeness and consistency of those requirements. It has allowed a means by which generalist software engineers can quickly come to terms with the essence of flight dynamics and its simulation for practical applications in the support and safety of aircraft operations. Keywords: reconfigurable flight simulations, flight dynamics, classical control theory, airworthiness certification, safety cases Background The successful materiel acquisition of an aircraft or its support systems is reliant on a detailed and clear knowledge of how to systematically specify: aircraft operational scenarios, aircraft flight dynamic performance, aerodynamic coefficients, sensitivity of avionics functionality and related training requirements. In the past government agencies and airlines purchased flight simulators (for pilot training) from organisations specialising in flight simulator development. Aerodynamic specialists within those organisations ensured the fidelity of operation and performance of simulators and correlated this performance with that of the actual aircraft being supported. New approaches to flight simulator development which allow purchase of end-user-reconfigurable flight simulators as commercial-off-the-shelf products [5], offer more broadly available solutions to the above problems but require a more detailed knowledge of flight dynamics and aerodynamics by the acquiring agency. Development of avionics, pilot training simulators and Fife support for each aircraft type, require that a suite of flight dynamic models be established. These models require a common, but tailored, traceability to the flight trial and aircraft design data. In the past it was often found that the basis of development and traceability of flight data was obscure, if not practically impossible to establish. Each model and its application would differ by diverse simulation fidelity requirements. It was observed that in many projects requiring flight dynamics the mathematical meaning of fidelity was not well understood. Neither do military standards on handling, or flight control systems design [1, 2, 3] or commercial standards [41 for flight simulator acceptance present an obvious structured approach to specifying flight dynamic performance. Further, safety-critical and safety related systems, inclusive of flight dynamics simulations, are becoming more highly integrated and continue to increase in complexity. In parallel with this, certification standards for such systems are becoming more stringent, requiring more extensive and more detailed analysis. Wilson, Kelly and McDermid [6] state: The purpose of a Safety Case is to provide a clear, cornprehensive and defensible argument supported by calculation and procedure that a system or installation will be acceptably safe throughout its life (and decommissioning).

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The requirement to clearly specify and justify design decisions relating to the flight dynamics for both the prime mission vehicle and its support equipments is obvious. Where flight simulators are used for development of mission critical avionic functions then this requirement translates to stringent airworthiness criteria to be applied to the development process, product functional design and product performance testing. Meeting the airworthiness safety requirements, specifying flight dynamics, and managing the family of various flight dynamic models cannot be generally be achieved without a structured, rigorous approach. Such an approach to the specification of underlying flight dynamics is therefore a critical enabling capability for successful acquisition and support. This paper presents such an approach to specifying flight dynamic performance and addresses the issue of specifying fidelity of simulation. It has been used in a practical application to train generalist software engineers working on a ground support software development facility for aircraft with modern second-generation avionics. The first section considers the importance of correct approach to modelling and simulating real-world phenomena. The second section uses the flight envelope as a basis for defining operational profiles and assessing test coverage at an operational level. The third section considers the specification of a point in the flight envelope and identifies the importance of the Characteristic Equation. The fourth section discusses the quantitative approach to measuring simulator fidelity from a stability perspective. Section 1: The modelling and measurement framework Rolf and Staples [7] provide a general strategy for specification, verification and validation of the simulation model and subsequent test of any model. Initial tests are performed in a wind tunnel on a scale model to derive aerodynamic coefficients typically for a rigid airframe. Flight trials are then conducted to confirm the coefficients and to derive adjustments to the rigid body data for effects such as flexure. Mathematical models are used to predict flight trial performance, emulate high fidelity handling characteristics, and replicate kinematic flight trajectories. A number of different conceptual models are available throughout the aircraft literature [see for example 8, 9, 10, 11]. These models can be used as a basis for simulator specification. The models provide general control laws and detail specific aerodynamic coefficients. General design guidance for military aircraft can also be found in military standards [2, 3]. Avionics test requirements are ultimately related back to the prime mission vehicle flight dynamic modelling. Other related models, of varing degrees of fidelity, are required for procedural simulators, the training of maintenance personnel, and for avionic software or hardware development. Assessment of sensor performance is also important in avionics development. The primary concern is to recreate the flight dynamic effects with sufficient fidelity so as to be able to test the integration of aircraft platform and sensors against performance of mission oriented algorithms. Reconfigurable flight simulators provide a means of achieving this, however a design characteristic of these simulators is a generic infrastructure which must be loaded with the correct aerodynamic data. The resulting simulated dynamic performance must then be validated against known aircraft performance, within defined limits with respect to the actual aircraft performance, and taking into account any accepted approximations. Flight trial data may result in up to three hundred data sets each of which may have from two to five parametric curves. The highest fidelity simulation model is usually in the Operational Flight Trainer (OFT) used to train pilots in the handling characteristics of the aircraft. In complexity it has approximately 250 aerodynamic coefficients represented as paramaterised graphs. By contrast, early avionics development models (circa 1980) were hard-coded had only -30 coefficients represented as a single numerical value. The present reconfigurable simulators may have -70 coefficients represented as parametric graphs and may be easily changed by use of a Graphical User Interface. Despite the increase in mathematical representation, for any one simulation- data set instantiation, it may only be possible to achieve adequate calibration of the simulator at one flight test point in the flight envelope. The large quantities of data, the many airframe configurations and combinations of environmental conditions requires an approach to specification and testing which is systematic, efficient and complete, also providing a well determined assessement of test coverage and fidelity of simulation within the flight envelope. Section 2: Operational Specification The aircraft flight envelope (expressing aircraft capability with respect to density altitude and speed (Mach Number) ) provides the first level of abstraction for defining operational capability. Military specification of flying qualities [2] identifies flight phase categories. When defining the simulation requirements the relevancy of each flight phase category should be considered and domains of the flight envelope identified in which each phase will be conducted. The military standard also requires: These flight phases shall be considered in the context of the total missions so that there will be no gap between successive phases of any flight and so that transition will be smooth. These two requirements lead to the ability to construct a graph, where the vertices (node) of the graph represents a specific operational performance condition of the aircraft within the flight envelope, and each edge represents a transition from one operational node to another node. The actual aircraft exhibits free-play with an infinite

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number of possible transitions between any two specified nodes. However the number of operational nodes specified for test needs to be kept sensibly to a minimum as the number of edges (transitions) for N nodes is given by the number of combinations of nodes taken two at a time, vis N(N-1)/2. Having identified the relevant nodes, consideration of how rapidly the aerodynamic coefficients may vary (due to physical parameters such as dynamic pressure, true airspeed, altitude etc.) needs to be made particularly when traversing edges of the operational graph. The flight envelope covers a very wide range of dynamic pressures (as low as 50 pound per square foot (psf) in the landing phase to pressures exceeding 2150 psf for Mach 1.2 at sea level). These variations in dynamic pressure may cause large changes in the aerodynamic coefficients. Equivalence partitioning is used to determine regions (a regime of continuous mathematics) of the flight envelope in which the physical parameters in question are constant or approximately so. Within the Flight Envelope the major speed partitions are: Subsonic, Transonic, and Super-sonic regions of flight. Major altitude partitions are the Troposphere and Stratosphere. The number of partitions will vary depending on the task at hand. For example on noe aircraft type examined experientially, the performance criteria were typically specified by use of graphs at nominally five different points within the flight envelope, whereas stability criteria were specified on a fine grid for each 0.1 Mach increment and typical altitudes of 0, 10,000, 20,000, 35,000 and 50,000 feet. This approach can sensibly minimise the number of physical test points required to span the flight envelope. The use of Boundary Value Analysis (BVA) is used as a testing strategy to specify the limits of the flight envelope. The physical strength limitations of an aircraft are presented as a V-n envelope with each aircraft having its own particular structural envelope. The flight operating strength of an aircraft is presented as a graph whose horizontal scale is airspeed (TAS or Mach Number) and whose vertical scale is load factor n. Aircraft strength is contingent on four parameters being known: the aircraft gross weight, the aircraft configuration (clean, flap configuration, gear, and stores); symmetry of loading, and altitude. The V-n diagram is not addressed further in this paper. Section 3: Specification of a performance point When each operational node is associated with an equivalence partition in the flight envelope the dynamic behaviour of the airframe may be specified. Aircraft motion involves the study of basic kinematics of a particle, and dynamic motion of both a rigid body and a body with flexure. The motion of an aircraft can be represented in its general form by a vector differential equation. Aircraft motion has six degrees of freedom, three associated with the translation of the aircraft center of gravity and three associated with rotation about the centre of gravity. The velocity vector [10, 11] of the aircraft can be used to generalise the description of its motion. The quality of the aircraft which tends to resist change in the velocity vector due to disturbance is what is known as stability and the quality which describes the ease with which the velocity vector may be changed is called control [10]. Within an equivalence partition aircraft configuration (flap scheduling, gear position, speedbrake deflection and stores configuration) also affect the performance. Each control surface (horizontal stabilators, rudders, ailerons, leading edge flap and trailing edge flap) will have an affect on the forces and moments acting on the airfame. The resulting motion is expressed in terms of non-linear differential equations, the rigorous solution of which is demanding even of current technology. Due to features such as the symmetry of the aircraft structure, the non-linear differential equations simplify [9,11] to linear differential equations of motion which usually decouple resulting in motion of the Longitudinal axis decoupled from that of the Lateral-Directional axes [11]. In accordance with this decoupling the avionics control systems for the aircraft are typically represented by a set of decoupled linear differential equations. This leads to a greatly simplified situation which may be effectively used by the generalist engineer to manage and understand the dynamics of the airframe without necessarily having aerodynamic specialty knowledge. The answer lies, in greater part, in an understanding of what is known as the 'Characteristic Equations'. Characteristic Equation To understand the significance of the Characteristic equation we briefly review the solution to a set of linear differential equations. The general form of an nth order linear differential equation is given by [13]:

Solving for y(t), the output function yields:

where

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1. ai, bj are constants, 2. f(t) represents the forcing or excitation function, and 3. y(t) is called the response function because it responds to the forcing function. The denominator is known as the Characteristic (Auxiliary) function of the differential equation. The Characteristic Equation results from setting the Characteristic function to zero. The Characteristic Equation provides a common paradigm for inter-disciplinary communications between those concerned with the mathematics of Differential Equations, and those concerned with the implementation of systems based on designs with Laplace Transforms and application of Modern Control Theory. As such different disciplines involved in avionics development such as mathematicians, aerodynamicists, flight control engineers and simulation experts can all understand the results presented. At each flight test point the aerodynamic coefficients are expanded in a process which is known as component buildup. A six degree of freedom aerodynamic model requires definition of basic coefficients for the following forces and moments [11]: Lift Force coefficient CL; Drag Force coefficient CD; Side Force coefficient CY; Rolling Moment coefficient CI; Pitching Moment coefficient Cm; Yawing Moment coefficient Cn. Basic coefficients are determined for translational velocities and are further modified for secondary and tertiary affects. When the aircraft is subjected to rotational velocities then modifications occur within the translational airflow and these perturbations are described by rate dependent coefficients [9, 10, 11, 12]. The coefficients of the Characteristic Equation are expressed as functions of the aerodynamic equations. The motion of each axis can now, through the coefficients of the Characteristic Equation, be related to the inertial components of the airframe and the forces and moments represented by the aerodynamic coefficients. To express the motion of the aircraft there are typically - 24 basic coefficients required for the Longitudinal axis and ~ 26 for the Lateral-Directional axes. Each coefficient may depend on angle of attack, angle of sideslip, mach number, air density, and altitude. Further, having decoupled the motion of the aircraft to its three principal axes, the notions of stability, controllability and manoeuvrability (elaborated below) can be independently applied within the limitations of decoupling approximations. Stability, Controllability and Manoeuvreability For each operational node (altitude, speed, normal 'g' load) within the Flight and n-V envelopes the overall aircraft performance may be quantitatively determined in terms of characteristics known as Stability, Controllability and Manoeuvrability. Stability analyses measure the airframe capability in a given configuration to remain in a prescribed state of operation (e.g. climb, cruise, descent etc.) It includes, if present, compensation by the Flight Controls Computer Stability Augmentation System. Stability is directly discernable to the pilot at the Man Machine Interface (MMI) interface as a combined airframe-flight controls response to small disturbances. Typical units of measure are natural mode frequencies and damping coefficients. These criteria can be expressed in the time domain as exponentially decaying sinusoids or in terms of the control theory paradigm utilising gain and phase margins. Controllability deals mainly with deliberate command inputs from the MMI and the subsequent airframe responses. Controllability transfer functions express airframe performance measures in terms of change in controlled variable per unit control input. Controllability characterises the feel of the controls in terms of either force or deflection of the control required to perform a particular manoeuvre, and Manoeuvrability issues express aspects of aircraft performance in terms of kinematic (e.g. climb rate, turn radius) or energy management capability (e.g. specific energy or specific excess power). The method proposed provides a quantitative basis for judging the more subjective and broader qualitative measure termed Handling [10, 11]. This paper will focus on the issue of quantitatively defining stability. Issues of controllability, manoeuvrability and handling requiring the foundation of stability are not a direct subject of this paper. General solution to the stability equations The general solution of the Characteristic Equations leads to a quantification of stability and fidelity of simulation, being the difference in performance of the programmed stability of the simulator compared with that of the real aircraft (as presented in the Flight Trials results). Longitudinal Stability It is observed [10, 11] that for the majority of aircraft types the stability of perturbed longitudinal motion can be expressed as a fourth degree polynomial

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which invariably factorises into two quadratic factors:

The first factor corresponds to a mode of motion which is characterised by an oscillation of long period. The mode is referred to as the phugoid mode. The second factor corresponds to a rapid relatively well damped motion associated with the short period mode. In some aircraft designs the solution to the phugoid mode may change from a damped oscillatory motion to a convergent and divergent mode. The divergent mode is characterised by the aircraft nose dropping in what is known as 'tucking under'. Lateral-Directional Stability It is observed [10, 11] that for the majority of aircraft types the stability of perturbed lateral-directional motion can be expressed as a fifth degree polynomial

which invariably factorises as follows:

The first term corresponds to the directional(heading) mode which is neutrally stable, i.e. there is no tendency for the aircrew heading to return to some previous equilibrium heading once the heading has been changed. The second term corresponds to the spiral convergence/divergence mode, which is a very slow motion corresponding to the tendency to maintain wings level or to roll off in a divergent spiral (typical time constants of-60 seconds). The third term corresponds to rolling subsidence mode describing the aircraft bank angie response to lateral inputs (typical time constants of 0.25 seconds). The fourth term is a quadratic called the 'Dutch roll' involving both rolling and yawing moments. The Dutch roll time constant is typically quite short (- 2 seconds) and the damping co-efficient quite low implying an oscillatory motion. These polynomials are the basis for systematically accounting for completeness of the specification of motion of the airframe at any given test point. They also permit the systematic measurement of the simulation of airframe performance. Section 4: Measuring Simulator Performance Fidelity Management of flight dynamics simulation typically requires two modes of control over the aircraft dynamics: 1.

Direct Control Mode. In this mode the aircraft dynamics are treated purely as kinematic, that is, without regard to force (and therefore moments) or mass, or

2.

Aerodynamic Force Mode. In this mode dynamic parameters are generated from a dynamic. force model incorporating aerodynamic and airframe characteristics.

The Characteristic Equations show that within aircraft dynamics second order equations predominate, implying step impulse, ramp and parabolic inputs can be used to bound responses during test. Provision of impulse, step, ramp and parabolic inputs to various parameters can be achieved through Direct Control Mode, placing the aircraft in trajectories and attitudes that may not be otherwise physically possible due to the inherent stability or instability of the airframe under aerodynamic load. For example, it may be required to investigate the sensitivity of the designate function (principally a longitudinal dependency) with respect to flight technical tolerances in roll and sideslip whilst maintaining a given heading and ground track. In the actual aircraft it may be impossible to achieve the required attitude except temporarily whereas under Direct Control Mode the attitude can be sustained. In other tests the stability of the aircraft may be the primary concern. For example the time required to achieve a given pitch attitude may be critical and this in turn depends on the Longitudinal stability of the aircraft. In these cases the Aerodynamic Force Mode would be used and it will be necessary to know how the performance of the simulation may differ from that of the actual baseline aircraft. For the purpose of testing avionics, it is usually the case that some aspects of full fidelity can be sacrificed dependent of the functional algorithm being

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tested. A sensitivity analysis is required for each function to be tested to determine which motions of the airframe may be significant to the problem at hand. These differences may be measured by plotting the roots of the Characteristic Equation of the actual aircraft and the simulator on an s-plane plot [10, 11, 13] as shown in Figure 4. In Figure 5 one of the modes of motion has been plotted as a measurement from the simulator and the second plot represents the performance as specified in the flight trial data. Comparison of the two plots allows the difference in simulation performance, or fidelity of simulation to be ascertained. This difference can be then assessed against the sensitivity analysis for the algorithm in question to see if the difference is significant. All modes of motion as identified from the characteristic equation must be accounted for in this way. If the difference in performance is considered significant then the aerodynamic coefficients of the simulator, and thus its Characteristic Equation, may be adjusted based on a sensitivity analysis of the algorithm under test. Conclusions In this paper we have demonstrated a systematic approach to the specification and management of reconfigurable flight simulator performance. The approach is applicable to requirements specification either in the acquisition, development or maintenance lifecycle phase of operation. Operational profiles are systematically defined by the use of graphs to specify aircraft performance nodes, and transitions between nodes, within the aircraft flight envelope. For each node specification of the airframe stability through the Characteristic Equations and their modes of oscillation is essential. This methodology intrinsically provides a measurement basis to assess simulator fidelity. The systematic methodology provides a greater level of design confidence that the problem-at-hand has been addressed fully. It significantly improves the ability of the generalist systems or solitaire engineer to understand, measure and calibrate the flight simulator performance with confidence that completeness and consistency of change has been addressed. The many seemingly disjoint components of the present civil and military standards can be placed into a cohesive context and their meaning and the inter-relationships between the different airframe response modes becomes clear. By adopting such an approach a higher degree of compliance in achieving safety critical aspects of Airworthiness Certification can also be assured and clear arguments in Safety Cases presentations can be constructed. This should result in lower development and testing effort and cost for safety critical sub-systems during development and maintenance phases of the aircraft life cycle.

1.

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2.

MIL-F-8785C, ‘Flying Qualities of Piloted Airplanes', Notice 1, 24 September 1991.

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MIL-F-9490D, ‘Flight Control Systems - Design, Installation and Test of Piloted Aircraft, General specification for’, Notice 1, 05 November 1992.

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AC120-40B, Simulator Standards, FAA, 15 May 1989.

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Virtual Prototypes Inc., Flight Simulator, FLSIM Software Design Document, March 1994.

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S.D. Wilson, T.P. Kelly, J.A. McDermid, “Safety Case Development: Current Practice, Future Prospects,” High Integrity Systems Engineering Group, University of York, York, Y01 5DD, UK, 1995

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Rolfe and Staples, 'Flight Simulation' Cambridge University Press, 1991.

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Stevens and Lewis, Aircraft Control and Simulation, Wiley Interscience 1992.

10. Donald McLean, Automatic Flight Control Systems, Prentice Hall, 1990. 11. Roskam, Airplane Flight Dynamics and Automatic Flight Controls, The University of Kansas, Lawrence, 66045 USA, 1994. 12. L. J. Clancy, 'Aerodynamics,' Longman Scientific and Technical, London, 1975. 13. Raven, 'Automated Control Engineering', McGraw

Hill 1968.

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