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Towards a Better Understanding of the Flight Mechanics of Compound Helicopter Configurations. Phd Thesis

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Towards a Better Understanding of the Flight Mechanics of Compound Helicopter Configurations. Phd Thesis Ferguson, Kevin M. (2015) Towards a better understanding of the flight mechanics of compound helicopter configurations. PhD thesis. http://theses.gla.ac.uk/6859/ Copyright and moral rights for this thesis are retained by the author A copy can be downloaded for personal non-commercial research or study This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the Author The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the Author When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given Glasgow Theses Service http://theses.gla.ac.uk/ [email protected] Towards a Better Understanding of the Flight Mechanics of Compound Helicopter Configurations Kevin M. Ferguson, B.Eng Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy November 6, 2015 School of Engineering College of Science and Engineering University of Glasgow © Kevin Ferguson, 2015 Abstract The compound helicopter is a high speed design concept that is once again being explored due to the emerging requirements for rotorcraft to obtain speeds that signifi- cantly surpass the conventional helicopter. The speed of the conventional helicopter is limited by retreating blade stall, however the introduction of compounding delays the onset of this aerodynamic limitation until greater flight speeds. There are two com- mon types of compounding known as lift and thrust compounding. Lift compounding, provided by the addition of a wing offloads the main rotor of its lifting responsibilities in high speed flight. Thrust compounding, provided by the addition of a propulsive source such as a propeller, provides additional axial force divorcing the main rotor of its propulsive duties at high speeds. The addition of compounding to the helicopter design can therefore increase the maximum speed of the aircraft. This increase in speed, pro- vided that efficient hover capability is maintained, would make the compound helicopter suitable for various roles and missions in both military and civil markets. The compound helicopter is not a novel idea with many compound helicopter con- figurations flight tested in the 1960's. Due to these test programmes, as well as other studies, there is some material relating to the compound helicopter in the literature. However, the majority of the compound helicopter work describes flight tests of ex- perimental aircraft or focuses on the design of the aircraft configuration. There are no systematic studies of the flight dynamics of compound helicopters which have been published. This Thesis targets this gap in the literature. Consequently, the aim of this Thesis is to investigate the effects of compounding on the conventional helicopter and how this addition to the helicopter design influences the flight mechanics of this aircraft class. With the renewed interest in the compound helicopter design this work is both original and timely. To investigate the flight dynamics of this aircraft class, two math- ematical models of compound helicopter configurations are developed and compared with a conventional helicopter. The first compound helicopter configuration features a coaxial rotor with a pusher propeller providing additional axial thrust, and is referred to as the coaxial compound helicopter. The second configuration, known as the hybrid compound helicopter, features two wings each with a tip mounted propeller providing i Abstract thrust compounding. The conventional helicopter features a standard helicopter de- sign with a main rotor providing the propulsive and lifting forces, whereas a tail rotor, mounted at the rear of the aircraft, provides the yaw control. Other authors have focused on design considerations and have quantified all of the benefits of compounding but to date, a comprehensive study of the effect of com- pounding on the flight dynamics of a helicopter has not been published. The strategy of the work is to take the three aircraft configurations, the two compound helicopter configurations and the conventional helicopter, and determine their flight mechanics characteristics. Subsequently, the compound helicopter results can be compared with the baseline configuration, thereby isolating the effects of compounding. The flight me- chanics characteristics that are determined in this Thesis include: trim, performance, stability and manoeuvrability attributes of the three helicopter configurations. These attributes are assessed by calculating the control angles which result in a steady flight condition and by the use of numerical linearisation and inverse simulation algorithms. All of these flight mechanics characteristics were assessed with the results, in some aspects, reinforcing the potential of the compound helicopter as well as highlighting some possible difficulties that will have to be addressed in the design of a compound helicopter. ii Nomenclature a Acceleration vector (m/s2) a0 Lift curve slope of a rotor blade element (1/rad) blade blade blade ax , ay , az Translational acceleration components of a rotor blade element in blade axes (m/s2) disc disc disc 2 ax , ay , az Acceleration components of the rotor hub in disc axes (m/s ) c Chord length (m) d¯ Drag per unit span (N/m) e Main rotor root cut out as a fraction of the rotor span blade faero Local aerodynamic force vector of a rotor blade element in blade axes (N/m) blade fel Force per unit span of a rotor blade element in blade axes (N/m) blade fin Local inertial force of a rotor blade element in blade axes (N/m) p.bl. fp Force of a propeller blade element in propeller blade axes, per unit span (N/m) anh fw Force of a wing strip in anhedral axes, per unit span (N/m) anh anh anh anh x , y , z Force components of the vector fw (N/m) p.bl. p.bl. p.bl. p.bl. fx , fy , fz Force components of fp (N/m) g Acceleration due to gravity (m/s2) h Altitude above mean sea level (m) hprop Height of the propeller hub from the reference point in body axes (m) hw Distance of the wing root above the centre of gravity (m) i; j; k Unit vectors k Empirical factor representing the main rotor's contribution to the wing iii Nomenclature lprop Length of the propeller hub from the reference point in body axes (m) ¯l Lift per unit span (N/m) lw Length from the vehicle reference point to the quarter chord position of a wing strip (m) m0 Mass per unit span of a rotor blade element in blade axes (kg/m) p.bl. mp Moment vector of a propeller blade element in propeller blade axes, per unit span anh mw Moment vector of the wing in anhedral axes, per unit span body mw Moment vector of the wing in body axes, per unit span n Propeller revolutions per second (rev/s) or load factor nclock Direction of rotational of the propeller p; q; r Small perturbations of angular velocities in body axes (rad/s) r Position vector (m) r¯ Normalised rotor blade position (m) body rc.g.!w Position vector from the centre of gravity to the quarter chord point of a wing strip in body axes (m) body body body body rx , ry , rz Components of the vector of rc.g.!w u Control vector (rad) u; v; w Small perturbations of translational velocities in body axes (m/s) p.d. p.d. p.d. p.d. u , v , w Translational components of vp.h. (m/s) v Velocity vector (m/s) v0; v1s; v1c Uniform and first harmonic rotor inflow terms (m/s) vi Induced velocity (m/s) v¯n Normalised normal velocity vn Normal velocity (m/s) p.d. vp.h. Velocity vector of the propeller hub in propeller disc axes (m/s) p.bl. vp Velocity vector at the quarter chord point of a propeller section in propeller disc axes (m/s) vres Resultant velocity across an aerofoil section (m/s) v¯tan Normalised tangential velocity vtan Tangential velocity (m/s) iv Nomenclature anh vw Velocity vector at the quarter chord point of a wing strip in anhedral axes (m/s) anh anh anh anh u , v , w Velocity components of the vector vw p.bl. p.bl. p.bl. p.bl. vx , vy , vz Components of the velocity vector vp wprop Lateral distance of the propeller hub from the reference point in body axes (m) x The state vector (varying units) x_ e,_ye,_ze Translational velocities in the Earth axes (m/s) xc.g. Centre of gravity position from the reference point (m) x_ Time derivative of the state vector yi Distance of the quarter chord point of a wing strip in the jb direction (m) A Rotor or propeller disc area, πR2 (m2) A, B The system and control matrices AR Wing aspect ratio C Coefficient blade Crot Normalised force vector of the main rotor in blade axes Cd Drag coefficient CDi Drag coefficient representing the induced drag of the wing CI Time-dependent damping matrix in individual blade flapping equations Cl Lift coefficient CL¯ Mean lift coefficient across the wing CM Time-dependent damping matrix in multi-blade flapping equa- tions 3 CP Power Coefficient, P/ρA(ΩR) 2 CQ Torque Coefficient, Q/ρAR(ΩR) 2 CT Thrust Coefficient, T/ρA(ΩR) CTL Lower rotor thrust coefficient CTU Upper rotor thrust coefficient 2 CW Weight Coefficient, W/ρA(ΩR) D Propeller diameter (m) DI Time-dependent stiffness matrix in individual blade flapping equations v Nomenclature DM Time-dependent stiffness matrix in multi-blade flapping equa- tions -1 DM 0 Constant stiffness matrix in multi-blade flapping equations body Fprop Force vector of the propeller in body axes (N) p.bl. Fprop Force vector of the propeller in propeller blade axes (N) body Frot Force vector of the main rotor in body axes (N) body Fwing Force vector of the wing in body axes (N) HI Time-dependent forcing function matrix in individual blade flapping equations HM Time-dependent forcing function matrix in multi-blade flapping equations -1 HM 0 Forcing function matrix in multi-blade flapping equations Ixx, Iyy, Izz Moments of inertia of the helicopter about the xb, yb and zb body axes (kgm2) 2 Ixy, Ixz, Iyz Products of inertia of the helicopter about the body axes (kgm ) 2 Iβ Flap moment of inertia (kg m ) J Propeller advance ratio, V=nD J Jacobian matrix Kβ Centre-spring rotor stiffness (N.m/rad) L, M, N The external moments about the xb, yb and zb body axes (N m) Lβ Transformation matrix from multi-blade to individual co-ordinates blade Lrot Rolling moment of the main rotor in blade axes (Nm) Lu, Lp, etc.
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