S. S. Houston

Validation of a Rotorcraft Mathematical Model for Autogyro Simulation

Results are presented from a study undertaken to validate a rotorcraft mathematical model for simulation of autogyro e ight. Although this class of rotary-wing aircraft has found limited application in areas other than sport or recreational e ying, commercial interest is increasing. A sparsecontemporary literature on autogyro e ight emphasizes the timeliness of this work, which takes advantage of e ight experiments using a fully instrumented autogyro.Validationisbasedoncomparisonsoftrim,linearizedsix-degree-of-freedomderivatives,andtimehistory response of the full nonlinear model to control inputs. The validation process is a vital ingredient in dee ning the applicability of a mathematical model as an engineering tool for supporting studies into aircraft stability, control, andhandlingqualities.Themodelisofgeneric,nonlinear,individualblade/bladeelementtype,anditscone guration as an autogyro is described. It is concluded that simulation of autogyro e ight presents no particular dife culties for a generic rotorcraft model. Limitations in predictive capability are clearly delineated, although in general comparisons between e ight and theory are good.

Analysis of rotorcraft flight dynamics in autorotation

Autorotation is a flight state whereby no powerplant torque is applied to the main rotor of a rotorcraft. For helicopters, autorotation is an abnormal mode of operation utilized in descending flight following total power failure. However it is the normal mode of operation for autogyros. It is common in helicopter mathematical modeling to assume constant rotorspeed, but this is invalid in autorotation. Introduction of the rotorspeed degree of freedom in modeling gives rise to an additional mode and coupling with the existing rigid-body modes. This paper therefore aims to explore the development of generic analytical expressions, exposing the role of the rotorspeed degree of freedom in modifying the classical rigid-body modes of motion. The analytical expressions are verified by quantifying their validity using autogyro derivatives obtained from a full nonlinear individual blade model. Comparison with the helicopter case then extends the generality and applicability of the analysis. It is concluded that there is an intimate relationship between the rotorspeed and low frequency rigid-body modes of rotorcraft in autorotation. The analytical expressions highlight the essence of coupled rotorspeed and rigid-body dynamics in autorotation, clearly identifying the conditions under which this relationship is stabilizing or otherwise.

IDENTIFIABILITY OF HELICOPTER MODELS INCORPORATING HIGHER-ORDER DYNAMICS

This paper examines the identification of a linearized mathematical model of a Puma helicopter from experimental data gathered during flight tests in hover. The objective has been to study the sensitivities of the model parameters to the choice of approach available. The model of the helicopter represents the vertical response of the aircraft to collective pitch, but has been extended to incorporate higher-order rotor dynamics associated with blade flapping and induced velocity degrees of freedom. The approaches used in the identification of the model are frequency-domain based: output error and transfer function matching of frequency responses identified using time series methods. Examples of the identification of helicopter models incorporating higher-order rotor dynamics using rotor measurements from flight data are new. It is concluded that models of helicopter behavior that include higher-order dynamics can be identified successfully from flight data, but engineering judgment is the key to successful application of the methods and interpretation of the results.

Modeling and analysis of helicopter flight mechanics in autorotation

Autorotation is an abnormal mode of operation for a helicopter because no powerplant torque is applied to the main rotor. Thus, descending e ight requires an upward e ow of air through the rotor to sustain rotation and, therefore, lift. There is a negligible literature on the e ight mechanics of helicopter autorotation, although the aerodynamic phenomenon is well understood. The objectiveof this paper is, therefore, to examinehelicopter e ight mechanics across the autorotation e ight envelope, while addressing the modeling requirements for simulation in autorotation. A nonlinear individual blade/blade element model of a conventional single main and tail rotor helicopteris used to generatea variety ofdata, including trim states, time,and frequency responses. It isconcluded that contemporary mathematical modeling can mimic the general performance characteristics of helicopters in autorotation with no special development. Although rotorspeed can vary signie cantly, even during maneuvers that embody only small perturbations in the body states, linearized models can remain an appropriate basis for analysis. Finally, distinctive aspects of helicopter e ight mechanics in autorotation, dissimilar to level e ight, are readily explained, and it is suggested that they are benign in nature.

Dynamic inflow modelling for autorotating rotors

The dynamic inflow model is a powerful tool for predicting the induced velocity distribution over a rotor disc. On account of its closed form and simplicity, the model is especially practical for studying flight mechanics or for designing control systems for helicopters. Scant attention has, however, been paid so far in utilising the dynamic inflow model to analyse an autorotating rotor, which is different from a powered rotor in the geometric relation between the direction of the inflow and the rotor disc. Autorotation is an abnormal condition for helicopters, but for gyroplanes it is the normal mode of operation. Therefore the theoretical discussion on an autorotating rotor is of importance not only to improve the understanding of present gyroplanes, but also in the development of new gyroplanes and to analyse the windmill-brake state of helicopters. Dynamic inflow modelling is reviewed from first principles, and this identifies a modification to the mass flow parameter. A qualitative assessment of this change indicates that it is likely to have a negligible impact on the trim state of rotorcraft in autorotation, but a significant effect on the dynamic inflow modes in certain flight conditions. This is confirmed by numerical simulation, although considerable differences only become apparent for steep descents with low forward speed. It is concluded that while modification of the mass flow parameter is perhaps mathematically accurate, for practical purposes it is required only in a limited area of the flight envelope of autorotating rotorcraft.

Application of Parameter Estimation to Improved Autogyro Simulation Model Fidelity

Development of an airworthiness design standard for light autogyros is underway in an attempt to improve a poor safety record. Mathematical modeling is playing a vital role in the understanding the flight mechanics of these rotorcraft. Unlike helicopters, autogyros have not received the attention of the technical community until recently, and, as a consequence, there is little theoretical analysis or experimental flight testing that makes use of contemporary methods. As a result, validity of mathematical modeling has relied on analysis of flight-test data from experiments conducted with two different aircraft. Parameter estimation by the use of a simple frequency-domain, equation-error approach has proved to yield consistent and robust results from each aircraft, highlighting the same mismatches between theory and experiment in both cases

Calculation of rotorcraft inflow coefficients using blade flapping measurements

Induced velocity gives rise to an important component of the angle of attack experienced by a blade element and, hence, the rotor loads. Finite-state induced-velocity models can be found in rotorcraft codes that require fast computation but cannot replicate real flowfield features. However, they do encapsulate in a simple and intuitive way the impact of real wakes on rotorcraft dynamics and hence are popular in codes that are used to study vehicle flight mechanics such as stability, control, and handling qualities. Explicit verification of these models is not possible, but implicit verification is possible if blade flapping is known; and this paper presents results from flight tests of a light gyroplane fitted with a two-bladed teetering rotor instrumented to measure the rotor flapping behavior. An appropriate model structure is developed to allow calculation of induced-velocity components from steady-flight flapping data recorded across the aircraft’s level-flight speed range. Very good agreement is obtained between flight and theory in respect to the uniform and longitudinal components, correlating well with previous studies. However, the lateral component is very poorly correlated, and this is attributed to strong nontrapezoidal behavior in the real wake. Notwithstanding this, it is concluded that the simple finite-state, induced-velocity model is a valid tool for gyroplane flight mechanics studies and rotorcraft autorotation in general.

Light gyroplane empennage design considerations

The light gyroplane is a class of aircraft popular with amateur constructors and pilots. As a result, there is limited design guidance available since formal technical resources are not available to the community. Rule-of-thumb, intuition and historical experience tend to influence design evolution. Empennage configuration is a prime example of this paradigm, and the objective of this Paper is to explore those factors that influence horizontal stabiliser effectiveness with particular reference to dynamic stability. An individual-blade rotorcraft mathematical model is coupled with a vorticity-based flowfield code, necessary to capture the highly interactional aerodynamics associated with empennage location at the rear of the airframe. A parametric study of horizontal stabiliser location shows that maximum benefit from the energising influence of the propeller slipstream is obtained if the surface is placed near the edge of the propeller wake. Further, traditional design parameters such as tail volume ratio offer an incomplete indicator of empennage effectiveness without consideration of airframe blockage and propeller slipstream. It is concluded that empennage sizing calculations can be straightforward, but require due consideration of the impact of the close-coupled nature of the vehicle on stabilising surface aerodynamic effectiveness.