Cyclic Pitch Research Articles

Time-periodic control of a multi-blade helicopter

Abstract : The flap-lag equations of motion of an isolated rotor blade and those for a rigid helicopter containing four blades free to flap and lag are derived. Control techniques are developed which stabilize both systems for a variety of flight conditions. Floquet theory is used to investigate the stability of a rotor blade's flap-lag motion. A modal control technique, based on Floquet theory, is used to eliminate the blade's instabilities using collective and cyclic pitch control mechanisms. The technique shifts the unstable roots to desired locations while leaving the other roots unaltered. The control, developed for a single design point, is shown to significantly reduce or eliminate regions of flap-lag instabilities for a variety of off-design conditions. Both scalar and vector control are successfully used to stabilize the blade's motion. Coupling the flap-lag equations of motion of four rotor blades to a rigid airframe alters the flap, lg, and airframes roots. The airframe roots are stabilized using a combination of the body's pitch attitude and pitch rate feedback to the main rotor's longitudinal cyclic pitch. The modal control technique is used to eliminate multiple blade instabilities by first controlling a pair of unstable roots at a specific design point. The resulting closed loop system is a new linear system which periodic coefficients. Another modal controller is designed for this new system to shift a second pair of unstable roots to desired locations. This process is repeated until all instabilities are eliminated. Numerical inaccuracies, however, become noticeable when modal control is used more than once.

Identification of State Variables and Dynamic Inflow From Rotor Model Dynamic Tests

The paper describes methods for extracting unknown state variables and parameters from dynamic rotor model tests given transient cyclic pitch stirring inputs, blade root flap-bending measurements, and the form of the dynamic rotor equations, including a rotor dynamic inflow description, when none of the physical parameters are known. A simplified version of the maximum likelihood method seems best suited for this purpose. The measurement equation error covariance matrix is assumed constant during each iteration, but updated for the subsequent iteration. A detailed analysis of the suitability of the derived techniques for studying various rotor dynamic inflow effects is provided.

An Unsteady Wake Model for a Hingeless Rotor

A simple nonsteady wake model derived from the unsteady moment of the momentum equation for zero advance ratio is correlated with cyclic pitch frequency response tests conducted with a small hingeless rotor model. Two and three or more bladed rotor analyses are presented.

Comment on "Derivation of the Thrust Equation from Conservation of Energy"

The dynamics of collective pitch changes are governed by Eq. (12) where it is seen that the parameter Kx, the virtual spring constant of the centrifugal force field depends on the inertia difference parameter (Iz Iy) and the initial pitch setting. Ordinarily z is negligible compared to c, so that this parameter is proportional to ccos2a-Q. Since CTQ is of the order of 45° at cruising flight speeds of 250 knots in the propeller state, the character of the dynamics are seen to change from that of a heavily damped oscillator (calculation of typical aerodynamic damping values yield values of the order of 50% of critical) in the hovering helicopter state when <JQ is a small angle to a cascaded integrator and time constant process. The dynamics of cyclic pitch change are governed by Eq. (17). Expansion of the system characteristic determinant shows that Kx is the critical parameter. In the hovering helicopter state the transient dynamics are those of a pair of coupled, damped oscillators. As a0 approaches 45° in the propeller-rotor state, a divergent oscillation ensues. It is evident that in the propeller-rotor cruise condition, both collective and cyclic pitch changes should have internal stabilization, the principal component of which would be proportional control action to offset the decreasing trend in Kx with forward speed. In the latter case of cyclic pitch change this is seen to be very important. Other compensation techniques would also be beneficial and would depend on the dynamics of the aircraft itself.

Complex Coordinates in Near Hovering Rotor Dynamics

The application of complex coordinates to the study of the dynamic characteristics of the tip-pathplane of a helicopter rotor is considered. The coordinates describing rotor blade motions can be transformed from individual blade flapping angles to linear combinations of flapping angles. Two of the transformed coordinates can be interpreted as describing the tilting motion of the tip-path-plane. In a stationary reference frame, these two new coordinates are coupled. However, by defining a set of complex coordinates, for near hovering flight these two coupled differential equations can be combined into a single second-order differential equation describing the tilting motion of the tip-path-plane. This formulation provides a convenient and natural framework for investigation of the response characteristics of fully articulated and hingeless rotors. Considerable insight into the influence of various physical parameters on the behavior of the tip-pathrplane can be gained. The approach is illustrated by consideration of the transient and frequency response characteristics of the tip-pathplane and the influence of flapping feedback. An extension of the root locus method is described which makes the investigation of flapping feedback convenient. Nomenclature! a - rotor blade lift curve slope b = number of blades A(s) = transfer function c = rotor blade chord Ci = rotor hub rolling moment coefficient, positive for right roll, Ci = L/pKR2(VR)2R Cm — rotor hub pitching moment coefficient, positive nose up, Cm = M/pirR2(QR)2R Cmz = complex rotor hub moment coefficient, Cmz— Cm + iCi /i = rotor blade flapping moment of inertia j = constant of proportionali ty between complex inflow and complex rotor aerodynamic hub moment coefficient KH = gain parameter associated with integral flapping feedback Kp,e = parameters associated with proportional flapping feedback mz — dimensionless aerodynamic moment acting on rotor blade due to forward speed. Effect of cyclic pitch, angular rates and flapping not included p = rotor blade natural frequency in flapping divided by rotor rpm, also roll rate nondimensionalized by rotor rpm, positive roll right q = pitch rate nondimensionalized by rotor rpm, positive nose up

Proprotor Short-Haul Aircraft-STOL and VTOL

This Paper examines the characteristics of a series of aircraft for the short-haul market. The low disk-loading propeller/rotor is applied to a prdpeller-STOL (short takeoff and landing) transport, a fan jet-STOL transport, a tilt rotor-VTOL (vertical takeoff and landing) transport, and a fan jet-VTOL transport. The resulting aircraft concepts have an efficient low-speed, lift-propulsion system, and can operate with low noise and air pollution from metropolitan V/STOL airports. This paper concentrates on the first two STOL configurations. For low and medium disk-loading STOL aircraft, the gimbal propeller Has important operational advantages compared to the rigid propeller. At takeoff, longitudinal cyclic pitch can be used to produce an upward force to reduce tail download requirements. For takeoff and landing in severe crosswinds, significant side force can be produced by means of lateral cyclic pitch. In cruise, the gimbal propellers give a significantly better ride than rigid propellers. In the approach, longitudinal cyclic pitch can control glide-slope height precisely. A STOL transport with a cruise speed of 400-500 knots (wing loading near 75 psf) could use the deflected slip-stream concept and medium disk-loading (30 psf), folding propeller/rotors (Frontispiece). Propulsion-system power requirements in both the cruise and low-speed mode would be supplied by convertible fan-shaft engines. This Paper shows the power balance between a twin fan-jet cruise requirement of 475 kt and an engine-out critical maneuver requirement at 60 knots.

Experimental aerodynamcis of a rotor entry vehicle.

An unpowered entry vehicle model has been tested at Mach numbers 0.10 to 3.54 at angles of attack from 15° to 90°. The tests included variations of blade collective and cyclic pitch angles. A summary of the autorotative equilibrium speed, forces, and moments is presented. The results indicate that adding the to the capsule improved vehicle performance throughout most of the Mach number range. Maximum lift drag ratio was substantially improved at low Mach numbers. Large pitching moments were produced by the rotor, requiring the use of flaps for longitudinal trim. Control phasing was unusual compared to the predicted response of an ideal rotor but did not change grossly with forward flight speed.

Dynamic analysis of the rigid rotor system.

A unified dynamic analysis for the rotor motion of the rigid or nonarticulated rotor system in a hovering state is presented. The dynamic behavior of the rigid rotor as well as that of the conventional rotor is expressed in a simple linearized mathematical form by using complex variables. The available control moment and the necessary phase shift for a given cyclic pitch input are obtained in general formulas and charts. Generally, the control and damping moments of the rigid rotor system increase with the increment of the napping stiffness, but there is a critical stiffness at which the aforementioned moments will be maximum. Optimum napping stiffness may be given so as to avoid unfavorable coupling motion between roll and pitch. It is not always necessary to install the control gyro, because similar stabilizing effect may be obtained by using the proper blade configuration without a special gyro system. The necessary control phase advance is also given to avoid cross control of the rigid rotor system.

Readers Forum: Comparative Response of Rotor Tip Path Plane to Longitudinal Cyclic Pitch and Changes in Rotor Angle of Attack

Readers Forum: Comparative Response of Rotor Tip Path Plane to Longitudinal Cyclic Pitch and Changes in Rotor Angle of Attack

A Note on the Effects of Longitudinal Cyclic Pitch Control Variations on the Forced Aero‐Elastic Response of a Helicopter Rotor Blade

A Note on the Effects of Longitudinal Cyclic Pitch Control Variations on the Forced Aero‐Elastic Response of a Helicopter Rotor Blade

Month in the Patent Office

A helicopter is propelled by a jet‐driven rotor 15 and a pair of turbine‐driven propellers 12 mounted on fixed stub wings 10, each rotor blade consisting of an inboard portion 20 mounted on the hub by a flapping and collective pitch‐adjusting hinge 22 and provided with a jet nozzle 24 at its outer end, together with an outboard portion 21 connected to the portion 20 by a cyclic pitch adjusting hinge 23. This arrangement enables the outboard blade portion 21, which contributes most of the lift, to be designed solely in accordance with aerodynamic considerations. Rods for controlling the outlet area of the nozzle 24 and for cyclic pitch adjustment of the blade portion 21 pass through the inboard portion 20. Gases for the propulsion units are supplied from a pair of gas turbines 14 through ducts 16, 18 provided with valves 17, 19 enabling the relative proportions supplied to the main rotor and propellers to be varied as desired.

A Type of Lifting Rotor with Inherent Stability

The more important of the forward flight aerodynamic characteristics of a rotor type are presented where the collective blade pitch angle is kinematically coupled with the collective flapping or coning angle, while no coupling is provided between cyclic flapping and cyclic pitch angles. The rotor with pitch-cone change may be designed to have positive static stability as compared to the negative static stability of the conventional fixedpitch rotor; partial blade stall during pull-ups or upward gusts may be avoided in spite of a high and economic thrust coefficient in steady flight, and no adjustment of the collective pitch control is required for the transition from powered flight to autorotation. The rotor with pitch-cone change, because of its inherent stability, promises, without recourse to external stabilizing devices, appreciably improved flying qualities of the helicopter.

The Disturbed Flapping Motion of Helicopter Rotor Blades

The article deals with the flapping motion of a helicopter blade when disturbed by external forces (gust, variation in cyclic pitch). The investigation is based on a rectangular and untwisted blade with the flapping hinge on the rotor axis. The disturbance gives rise to nonperiodic oscillations, which are described by a linear differential equation with periodic coefficients. In solving this equation, a criterion is obtained which permits rapid determination of the conditions of stability. Numerical evaluation shows that the disturbed motion is stable, though at a certain critical advance ratio partial destabilization sets in which increases with increasing flying speed. The influence of coupling between flapping angle and blade pitch is also considered. Practically, the disturbed motion is finished after one revolution of the rotor.