Adding In-Plane Flexibility to the Equations of Motion of a Single Rotor Helicopter

Adding In-Plane Flexibility to the Equations of Motion of a Single Rotor Helicopter

Author: National Aeronautics and Space Adm Nasa

Publisher: Independently Published

Published: 2018-09-25

Total Pages: 40

ISBN-13: 9781724040121

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This report describes a way to add the effects of main rotor blade flexibility in the in- plane or lead-lag direction to a large set of non-linear equations of motion for a single rotor helicopter with rigid blades(l). Differences between the frequency of the regressing lag mode predicted by the equations of (1) and that measured in flight (2) for a UH-60 helicopter indicate that some element is missing from the analytical model of (1) which assumes rigid blades. A previous study (3) noted a similar discrepancy for the CH-53 helicopter. Using a relatively simple analytical model in (3), compared to (1), it was shown that a mechanical lag damper increases significantly the coupling between the rigid lag mode and the first flexible mode. This increased coupling due to a powerful lag damper produces an increase in the lowest lag frequency when viewed in a frame rotating with the blade. Flight test measurements normally indicate the frequency of this mode in a non-rotating or fixed frame. This report presents the additions necessary to the full equations of motion, to include main rotor blade lag flexibility. Since these additions are made to a very complex nonlinear dynamic model, in order to provide physical insight, a discussion of the results obtained from a simplified set of equations of motion is included. The reduced model illustrates the physics involved in the coupling and should indicate trends in the full model. Curtiss, H. C., Jr. Ames Research Center


Coupled Rotor-Body Equations of Motion Hover Flight

Coupled Rotor-Body Equations of Motion Hover Flight

Author: National Aeronautics and Space Administration (NASA)

Publisher: Createspace Independent Publishing Platform

Published: 2018-07

Total Pages: 46

ISBN-13: 9781722135423

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A set of linearized equations of motion to predict the linearized dynamic response of a single rotor helicopter in a hover trim condition to cyclic pitch control inputs is described. The equations of motion assume four fuselage degrees of freedom: lateral and longitudinal translation, roll angle, pitch angle: four rotor degrees of freedom: flapping (lateral and longitudinal tilt of the tip path plane), lagging (lateral and longitudinal displacement of the rotor plane center of mass); and dynamic inflow (harmonic components). These ten degrees of freedom correspond to a system with eighteen dynamic states. In addition to examination of the full system dynamics, the computer code supplied with this report permits the examination of various reduced order models. The code is presented in a specific form such that the dynamic response of a helicopter in flight can be investigated. With minor modifications to the code the dynamics of a rotor mounted on a flexible support can also be studied. Curtiss, H. C., Jr. and Mckillip, R. M., Jr. Unspecified Center NAG2-561...


Method for Studying Helicopter Longitudinal Maneuver Stability

Method for Studying Helicopter Longitudinal Maneuver Stability

Author: Kenneth B. Amer

Publisher:

Published: 1953

Total Pages: 62

ISBN-13:

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Good correlation is indicated for both a single-rotor helicopter and a tandem-rotor helicopter between manuever stability as predicted by the chart and as measured during pull-up maneuvers. Thus, the theoretical analysis is indicated to be valid.


Prediction of Rotor Instability at High Forward Speeds. Volume I. Steady Flight Differential Equations of Motion for a Flexible Helicopter Blade with Chordwise Mass Unbalance

Prediction of Rotor Instability at High Forward Speeds. Volume I. Steady Flight Differential Equations of Motion for a Flexible Helicopter Blade with Chordwise Mass Unbalance

Author: Peter J. Arcidiacono

Publisher:

Published: 1969

Total Pages: 73

ISBN-13:

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The differential equations of motion for a linearly twisted rotor blade having chordwise mass unbalance and operating under steady flight conditions are derived. The motions include flapping and lagging for the articulated blade, as well as flatwise, edgewise, and torsional deformations for the articulated and nonarticulated blades. The fully coupled aerodynamic forcing functions are based on quasi-steady theory. The differential equations of motion are expanded in terms of the uncoupled vibratory modes of the blade in order to facilitate their numerical solution on a digital computer. (Author).


Foundations of Helicopter Flight

Foundations of Helicopter Flight

Author: S. Newman

Publisher: Elsevier

Published: 1994-04-07

Total Pages: 317

ISBN-13: 0080928544

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The unique design problems which helicopters produce are many and complex. Through practical examples and illustrated case studies, supported by all the relevant theory, this primer text provides an accessible introduction which guides the reader through the theory, design, construction and operation of helicopters. Fundamental performance and control equations are developed, from which the book explores the rotor aerodynamic and dynamic characteristics of helicopters. Example calculations and performance predictions, reflecting current practice, show how to assess the feasibility of a design.* Tackles the theory, design, construction and operation of helicopters* Illustrated with many practical examples and case studies* Provides the fundamental equations describing performance and dynamic behaviour


Flight Test Determination of Lateral Stability and Control Derivatives for a Single Rotor Helicopter. Part I. Equations of Motion, Analysis Techniques, Instrumentation, and Flight Shakedown

Flight Test Determination of Lateral Stability and Control Derivatives for a Single Rotor Helicopter. Part I. Equations of Motion, Analysis Techniques, Instrumentation, and Flight Shakedown

Author: W. R. Deazley

Publisher:

Published: 1959

Total Pages: 132

ISBN-13:

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The lateral equations of motion were derived for the single rotor helicopter considering three rigid-body degrees of freedom. Means are presented for estimating the various physical and aerodynamic characteristics of the XHO3S-2 helicopter. Sample calculations are made in which the stability derivatives are found for the 70 mph case. Methods are presented for etracting the primary lateral aerodynamic stability derivatives from helicopter flight test data. Both steady-state and transient flight test methods were considered. The contributions of the various terms in the equations of motion to the lateral responses of the helicopter were studied on an analog computer. Both lateral cyclic pitch and tail rotor collective pitch step inputs were used for exciting the various lateral modes of the helicopter. Certain new instrumentation was developed to measure the necessary lateral variables. A complex strain gage installation measures the resolved lateral shear and moments in the rotor shaft. (Author).