High-speed Forward Flight Research Articles

On the effects of rotor induced vibrational stability on helicopter flight dynamics

This article investigates vibrational stabilization effects in rotorcraft flight dynamics. This study is motivated by recent results in flapping-wing flight, which showed that the time-varying aerodynamic and inertial loads due to the insect wing periodic motion induce a vibrational stabilization mechanism in hover. The dynamics of flapping-wing flyers and rotary-wing vehicles are both described by time-periodic systems so vibrational stabilization mechanisms can also have an effect on stability characteristics of rotary-wing vehicles. The article extends the use of the harmonic decomposition method to vibrational stability analysis of rotorcraft. Two cases are considered: vibrational stability due blade imbalance at hover, and vibrational stability due to number-of-blades-per-rotor-revolution (Nb\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_b$$\\end{document}/rev) in high-speed forward flight. Results show that while vibrations induced by rotor blade imbalance do not stabilize the hovering dynamics of a helicopter, these vibrations can still have a significant effect on the hovering dynamics. Rotor blade imbalance results in a symmetric effect on the roll and pitch axes, in that it tends to decrease the frequency of the subsidence modes of the hovering cubic, while the unstable oscillatory modes tend to increase in frequency and decrease in damping (destabilizing effect). On the other hand, the yaw/heave dynamics are relatively unaffected compared to the lateral and longitudinal axes. Moreover, Nb\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_b$$\\end{document}/rev rotor loads in forward flight are shown to reduce the damping of the coupled roll/pitch oscillation mode.

Rotor Power Savings and Pitch-Link Load Reductions with Spanwise-Varying Active Camber Morphing

The effect of spanwise-varying active-camber morphing on helicopter rotor power and pitch-link loads was investigated computationally for advance ratios ranging from hovering to high-speed forward flight (μ=0.35) and was compared to results obtained with spanwise uniform camber actuation. Different actuation strategies were applied, such as constant (0P) deflection and superimposed harmonic actuation based on a 0P deflection combined with 1P (one per revolution) and 2P harmonics. A comprehensive rotor aeromechanics model of an isolated Bo-105 rotor, including elastic blade modeling and free vortex wake aerodynamics, was used for this analysis. Two different active-camber section sizes were investigated, one ranging from 0.22R to 0.9R and one from 0.5R to 0.9R. The greatest benefits from active-camber actuation were found in hover and high-speed flight. It was possible to reduce both the rotor power consumption and the peak-to-peak pitch-link loads. A relevant contribution of the spanwise variability to these power gains was obtained in hovering flight. Toward higher flight speeds, the effect of spanwise variable camber morphing became less important in terms of rotor power savings. However, it allowed a notable reduction of the actuation amplitude far outboard on the rotor blade.

Full envelope nonlinear flight controller design for a novel electric VTOL (eVTOL) air taxi

AbstractOn-demand urban air transportation gains popularity in recent years with the introduction of the electric VTOL (eVTOL) aircraft concept. There is an emerging interest in short/medium range eVTOL air taxi considering the critical advantages of electric propulsion (i.e. low noise and carbon emission). Using several electric propulsion systems (distributed electric propulsion (DEP)) has further advantages such as improved redundancy. However, flight controller design becomes more challenging due to highly over-actuated and coupled dynamics. This study defines and resolves flight control problems of a novel DEP eVTOL air taxi. The aircraft has a fixed-wing surface to have aerodynamically efficient cruise flight, and uses only tilting electric propulsion units to achieve full envelope flight control via pure thrust vector control. The aircraft does not have conventional control surfaces such as aileron, rudder or elevator. Using pure thrust vector control has some design benefits, but the control problem becomes more challenging due to the over-actuated and highly coupled dynamics (especially in transition flight). A preliminary flight dynamics model is obtained considering the dominant effects at hover and high-speed forward flight. Hover and forward flight models are blended to simulate the transition dynamics. Two central challenges regarding the flight control are significant nonlinearities in aircraft dynamics during the transition and proper allocation of the thrust vector control specifically in limited control authority (actuator saturation). The former challenge is resolved via designing a sensor-based incremental nonlinear dynamic inversion (INDI) controller to have a single/unified controller covering the wide flight envelope. For the latter one, an optimisation-based control allocation (CA) approach is integrated into the INDI controller. CA requires special attention due to the pure thrust vector control’s highly coupled dynamics. The controller shows satisfactory performance and disturbance rejection characteristics. Moreover, the CA plays a vital role in guaranteeing stable flight in case of severe actuator saturation.

CFD analysis on the performance of a coaxial rotor with lift offset at high advance ratios

The aerodynamic performance of an isolated coaxial rotor in forward flight is analyzed by a high-fidelity computational fluid dynamics (CFD) approach. The analysis focuses on the high-speed forward flight with an advance ratio of 0.5 or higher, which is the ratio of the forward speed to the rotor tip speed. The effect of the degree of the rolling moment on the rotor thrust, called lift offset, is studied in detail. The coaxial rotor model is a pair of contrarotating rotors, each rotor consisting of two untwisted blades with a radius of 1.016 m. The pitch angle of the blades is controlled by both collective and cyclic as in a conventional single main-rotor helicopter. CFD analysis is performed using a flow solver based on the compressible Navier-Stokes equations with a Reynolds-averaged turbulence model. Laminar/turbulent transition in the boundary layer is taken into account in the calculation. The rotor trim for target forces and moments is achieved using a gradient-based delta-form blade pitch angle adjusting technique in conjunction with CFD analysis. The reliability of the calculations is confirmed by comparison with published wind tunnel experiments and two comprehensive analyses. Applying the lift offset improves the lift-to-effective drag ratio (lift-drag ratio) and reduces thrust fluctuations. However, in the case where the advance ratio exceeds 0.6, the lift-drag ratio drops significantly even if the lift offset is 0.3. The thrust fluctuation also increases with such a high advance ratio. Detailed analysis reveals that the degradation of aerodynamic performance and vibratory aerodynamic loads is closely related to the pitch angle control to compensate for the reduction in thrust on the retreating side due to the increased reverse flow region. It is effective to reduce the collective and longitudinal cyclic pitch angles for the improvement of the aerodynamic performance of coaxial rotors with an appropriate lift offset.

Flight Performance with Respect to Rotor Rotation Directions of Multirotor Aircraft

A multirotor electric vertical takeoff and landing (EVTOL) aircraft is specialized for intracity point-to-point urban air mobility services due to its advantages of efficient hover performance, high gust resistance, and relatively low noise. Because of its multiple rotors, rotor–rotor interference inevitably affects flight performance, mainly depending on inter-rotor distance and rotor rotation directions. It is assumed that there exists an optimal rotation direction for a given lot of multiple rotors. In this study, the aim is to investigate rotor–rotor interference for various rotation directions and the resulting flight performance. We propose a concept of rotor rotation direction that achieves the desirable flight performance in forward flight. The concept is called front-retreating/rear-advancing (FRRA), in which the retreating side of the front rotor and the advancing side of the rear rotor are aligned in a straight line. To this end, a multidisciplinary flight simulation framework was developed to predict the flight performance of a general multirotor EVTOL aircraft. It was found that the FRRA concept minimizes thrust loss due to rotor–rotor interference in high-speed forward flight. For a generic mission profile, the rotation direction set by the FRRA concept reduces the battery energy consumption by 7% in comparison to the rotation direction of unfavorable rotor–rotor interference in operation.

CFD-CSD method for rotor aeroelastic analysis with free wake model

PurposeComputational fluid dynamics (CFD)/computational structural dynamics (CSD) coupling analysis is an important method in the research of helicopter aeroelasticity due to its high precision. However, this method still suffers from some problems, such as wake dissipation and large computational cost. In this study, a new coupling method and a new air load correction method that combine the free wake model with the CFD/CSD method are proposed to maintain computational efficiency whilst solving the wake dissipation problem of the prior coupling methods.Design/methodology/approachA new coupling method and a new air load correction method that combine the free wake model with the CFD/CSD method are proposed. With the introduction of the free wake model, the CFD solver can adopt two-order accuracy schemes and fewer aerodynamic grids, thus maintaining computational efficiency whilst solving the wake dissipation problem of the prior coupling methods.FindingsCompared with the predictions of the prior methods and flight test data, those of the proposed method are more accurate and closer to the test data. The difference between the two methods in high-speed forward flight is minimal.Research limitations/implicationsBecause of the chosen research approach, the research results may lack generalisability. Therefore, researchers are encouraged to test the proposed method further.Originality/valueIn this paper, a CFD/CSD/free wake coupling method is proposed to improve the computational accuracy of the traditional CFD/CSD coupled method and ensure the computational efficiency.

Aeroelastic Tailoring of the Next Generation Civil Tiltrotor Technological Demonstrator Composite Wing

The tiltrotor wing structure is one of the most critical and heavily investigated structures in design due to the fundamental need to consider the interactions between the wing, pylon, and rotor systems to achieve aircraft aeroelastic stability. Indeed, in high-speed forward flight, wing flexural and torsional stiffness have fundamental roles in pitch-whirl stability. Another specific concern of tiltrotors is dynamic mode placement; it is necessary to properly place wing bending modes away from prop-rotor forcing frequencies. The main aeroelastic stability and dynamics requirements and the wing design process flow for the next generation civil tiltrotor are presented in this work. In this context, the use of composite materials plays a fundamental role in the attempt to satisfy the requirements, with the perpetual aim of minimizing the structural weight. An overview of the idealized and adopted models for strength, aeroelasticity, and whirl flutter analysis is provided. The primary focus was on the aeroelastic tailoring process. To satisfy, at the same time, all of the structural dynamic and aeroelastic stability requirements, the best compromise, with an acceptable weight penalty, was the mixture of two methodological solutions: adding unidirectional tape in the zones of the upper and lower skins for flexural out-of-plane frequency and adding a proper number of ±45° fabric layers at the locations of the skin with the highest value of strain energy for in-plane torsional modes. The results show that the proposed method based on modal strain energy analysis enables a tiltrotor aeroelastic tailored wing design. It can be easily employed in similar applications (e.g., vehicle scale-up/down) with the advantage of using the stiffness requirements derived directly from the aeroelastic ones (i.e., structural frequencies). The specific wing achieved aeroelastic clearance by adding only 2.7% of extra mass.

Interactional Aerodynamic Analysis of an Asymmetric Lift-Offset Compound Helicopter in Forward Flight

Recently, an asymmetric lift-offset compound helicopter has been conceptualized at the University of Maryland with the objective of improving the overall performance of a medium-lift utility helicopter. The investigated form of lift-compounding incorporates an additional stubbed wing attached to the fuselage on the retreating side. This design alleviates rotor lift requirements and generates a roll moment that enables increased thrust potential on the advancing side in high-speed forward flight. In this study, a numerical model was developed based on the corresponding experimental test case. Threedimensional unsteady Reynolds-averaged Navier–Stokes equations were solved on overset grids with computational fluid dynamics–computational structural dynamics (CFD–CSD) coupling using the in-house CPU–GPU heterogeneous Mercury CFD framework. Simulations were performed at high-speed, high-thrust operating conditions and showed satisfactory agreement with the experimental measurements in terms of the cyclic control angles, rotor thrust, and torque values. CFD results indicated that for an advance ratio of 0.5 with a collective pitch of 10.6°, a vehicle lift-to-equivalent-drag ratio improvement of 47% was attainable using 11% wing-lift offset. The CFD-computed flow fields provide insights into the origin of a reverse flow entry vortex that was observed in particle image velocimetry data, and they characterize the wing–rotor interactional aerodynamics.

MPC Flight Control for a Tilt-Rotor VTOL Aircraft

This article presents a model predictive control (MPC) controller and its novel application to a hybrid tilt-quadrotor fixed-wing aircraft, which combines vertical takeoff and landing (VTOL) capabilities with high-speed forward flight. The developed MPC controller takes a velocity command from the pilot and then computes optimal attitude setpoints and propeller-tilt angles that are supplied to a fast inner attitude controller. A control allocation algorithm then maps the output of the inner attitude loop to actuator commands. The proposed MPC and control allocation of this article constitute a unified nonlinear control approach for tilt-rotor VTOL aircraft, valid in all flight modes and transitions in between. The whole approach is verified both in simulations and in real-world outdoor experiments with a remote controlled VTOL aircraft transitioning from hover to high speed and vice versa in a stable and controlled manner. Results show superior performance compared to the common binary-switch transition strategy between multicopter flight mode and the fixed-wing flight mode. The MPC controller also consistently performs better than a previously developed fused-PID control architecture in our tests.

Geometry Design of Coaxial Rigid Rotor in High-Speed Forward Flight

The aerodynamic performance analysis and blade planform design of a coaxial rigid rotor in forward flight were carried out utilizing CFD solver CLORNS. Firstly, the forward flow field characteristics of the coaxial rotor were analyzed. Shock-induced separation occurs at the advancing side blade tip and severe reverse flow occurs at the retreating side blade root. Then, the influence of geometrical parameters of the coaxial rigid rotor on forward performance was investigated. Results show that swept-back tip could reduce the advancing side compressibility drag and elliptic shape of blade planform could optimize the airload distribution at high advance ratio flights. A kind of blade planform combining swept-back tapered tip and nonlinear chord distribution was optimized to improve the rotor efficiency for a given high-speed level flight based on geometric parameter studies. The optimized coaxial rotor increases lift-to-drag ratio by 30% under the design conditions.

Aerodynamically induced noise of a lift-offset coaxial rotor with pitch attitude in high-speed forward flight

This paper investigates both acoustics and performance of a lift-offset coaxial rotor based on a first-principles and high-fidelity CFD (Computational Fluid Dynamics) and CSD (Computational Structural Dynamics) loose coupling approach in high-speed forward flight at different vehicle pitch attitudes. The pitch attitudes selected for this research are −5∘, 0∘, and 5∘. Detailed aerodynamic analyses are performed at two flight speeds: 150 (278 km hr−1) and 200 knots (370 km hr−1). A total of six major unsteady aerodynamic interactions are identified: 1) hub-wake interaction, 2) self-BVI (blade-vortex interaction), 3) parallel rotor-to-rotor BVI, 4) blade-crossover events, 5) root-induced BVI, and 6) reversed-flow-edge-vortex interactions. The strength of these interactions is found to be dependent on vehicle pitch attitude. The cases with a negative pitch attitude show significantly stronger impulsive pressure pulses, which is found to be induced by parallel rotor-to-rotor BVIs of the lower rotor. It is shown that the positive and zero pitch attitude cases tend to dominate the acoustic region on the starboard side of the coaxial rotor, whereas the negative pitch attitude case shows higher acoustic pressure peaks on the port side. Overall, the high-speed case with a positive pitch attitude shows significant improvement in rotor aerodynamic efficiency, rotor acoustics, and vehicle power performance at high speed. The hemispherical acoustic simulation results also show that the noise is less likely to propagate in the forward direction at a positive pitch attitude in high-speed forward flight.

Aeromechanics Analyses of a Modern Lift-Offset Coaxial Rotor in High-Speed Forward Flight

This study conducts an aeromechanics analysis of a modern lift-offset coaxial rotor in high-speed flight. A lift-offset coaxial rotor of the Sikorsky X2 technology demonstrator (X2TD) is considered for the present study. For the analyses of rotor performance, blade airloads, and hub vibratory loads, a rotorcraft comprehensive analysis code, CAMRAD II, is used. For the rotor performance analysis at a flight speed of up to 250 knots, which is the maximum level flight speed of X2TD in flight test, the present prediction of rotor power is compared well with the flight test data. For the blade section airload analysis at 250 knots, the impulses of the section lift forces are observed because of the aerodynamic interactions between the upper and lower rotors. The 4/rev hub vibratory loads are predicted, and its variation trend is moderately compared with the previous analysis results. Furthermore, the rotor vibration index increases significantly in high-speed flight with an increase in the flight speed, and this is well correlated with the previous rotorcraft comprehensive analysis result. This study shows that the present modeling and analysis techniques are appropriate to analyze the aeromechanics, including the performance, blade airloads, and hub vibratory loads of a modern lift-offset rotor in high-speed flight.

Assessment of current rotor design comparison practices based on high-fidelity CFD methods

ABSTRACTThis paper provides an assessment of current rotor design comparison practices. First, the employed CFD method is validated for a number of rotor designs and is shown to achieve accurate performance predictions in hover and high-speed forward flight. Based on CFD results, a detailed investigation is performed in terms of comparing different rotor designs. The CFD analysis highlighted the need of high fidelity methods due to the subtle aerodynamics involved in advanced planforms. Nevertheless, the paper suggests that the correct basis for comparison in terms of performance metrics must be used to inform decisions about the suitability of the rotor blades designs for specific applications. In particular, when comparing blades of advanced planforms, direct torque and thrust comparisons are better than the commonly used lift to drag ratio and figure of merit.

Impulsive Loading Noise of a Lift-Offset Coaxial Rotor in High-Speed Forward Flight

This study was conducted to investigate the impulsive acoustic characteristics of a lift-offset coaxial rotor in high-speed forward flight, as well as the impact of wake-grid resolution and turbulence modeling on acoustic prediction. High-fidelity computational fluid dynamics/computational structural dynamics loose-coupling simulations were performed for air-load prediction using the high-fidelity rotorcraft aeromechanics simulation software Helios, and impulsive loading noise was simulated using the acoustic prediction software PSU-WOPWOP at eight microphones positioned below the lower rotor plane. No significant discrepancy in air-load and acoustic predictions was found between the three turbulence modeling cases [Spalart–Allmaras (SA)–Reynolds-averaged Navier–Stokes, SA–detached-eddy simulation, and SA–delayed-detached-eddy simulation] with . It was found that the case showed a good convergence of impulsive loading noise at most microphones in terms of the wake-grid resolution. Isolated rotor simulations were also carried out to quantify the relative importance of the two impulsive loading-noise sources of a lift-offset coaxial rotor: self-blade–vortex interaction (BVI) and blade-crossover events. Contours of induced inflow ratio on the rotor disks revealed higher induced velocity for the lift-offset coaxial rotor than the isolated rotors. The higher induced flow ratio reduced the distribution of sectional normal force, strength of self-BVIs, and BVI noise of the lift-offset coaxial rotor. Even with the reduced BVI noise, the lift-offset coaxial rotor showed a dramatically higher impulsive sound-pressure level than the isolated rotors, especially at high speed, as a consequence of mainly blade-crossover events.

Vibration and Performance Analyses Using Individual Blade Pitch Controls for Lift-Offset Rotors

This work attempts to reduce the hub vibratory loads of a lift-offset rotor using IBC (individual blade pitch control) in high-speed forward flight. As a lift-offset rotor for the present study, the rigid coaxial rotor of a XH-59A compound helicopter is considered and CAMRAD II is used to predict the hub vibration and rotor performance. Using the IBC with a single harmonic input at 200 knots, the vibration index of the XH-59A rotor is minimized by about 62% when the 3/rev actuation frequency is applied with the IBC amplitude of 1° and control phase angle of 270° (3P/1°/270°); however, the rotor effective lift-to-drag ratio decreases by 3.43%. When the 2/rev actuation frequency with the amplitude of 2° and control phase angle of 270° (2P/2°/270°) and the 3/rev actuation frequency using the magnitude of 1° and control phase angle of 210° (3P/1°/210°) are used in combination for the IBC with multiple harmonic inputs, the vibration index is reduced by about 62%, while the rotor effective lift-to-drag ratio increases by 0.37% at a flight speed of 200 knots. This study shows that the hub vibration of the lift-offset rotor in high-speed flight can be reduced significantly but the rotor performance increases slightly, using the IBC with multiple harmonic inputs.

Modeling and Adaptive Control for Multirotor Subject to Thruster Dynamics

Research on high-speed flight dynamics of multirotors is in increasing demand for “quick-reach” missions such as short-distance delivery and disaster assessment. The conventional works have integrated a linear thruster model in the dynamics modeling stage and developed a corresponding control algorithm; however, the linear thruster assumption has been shown to be accurate only in a near-hover state through wind tunnel tests. This paper proposes a novel multirotor dynamics model incorporating blade element momentum theory (BEM), which can precisely predict transient thruster output in various flight states (e.g., no flow, oblique flow, and pure side flow). With the proposed dynamics model, degradation of control performance caused by disturbances and variations is noticed under typical flight state (e.g., high-speed forward flight and drastic vertical rising). Finally, an adaptive robust backstepping control algorithm is proposed to achieve guaranteed performance under the aforementioned variations and disturbances. The simulations are carried out on a small quadrotor to verify the proposed approach.

Aeroelastic modelling and stability analysis of tiltrotor aircraft in conversion flight

ABSTRACTIn conversion flight, the aeroelastic modelling of tiltrotor aircraft needs to consider the unsteady effect of the rotor wake bending due to the rotor tilting. In this paper, the unsteady models of the rotor wake bending and dynamic inflow have been introduced into the aeroelastic modelling of the tiltrotor aircraft in conversion flight by using Hamilton’s generalized principle. The method for solving the aeroelastic stability of tiltrotor aircraft in conversion flight has been established by using the small perturbation theory and the Floquet theory. The influences of unsteady dynamic inflow on trim control inputs and aeroelastic stability of a tiltrotor aircraft in conversion flight were calculated and analysed. The calculation results show that the required collective pitch increases with the pylon tilting forward and the unsteady inflow is trimmed primarily by the lateral cyclic pitch of the rotor. The wake bending unsteady dynamic inflow can obviously reduce the stability of the flapping modes of the rotor, and have no obvious influence on the lag modes of the rotor and the motion modes of the wing. The instability of tiltrotor occurs in the chordwise bending mode of the wing when the pylon tilts to a certain angle in high speed forward flight.

Aeroacoustic Analysis of a Lift-Offset Coaxial Rotor Using High-Fidelity CFD/CSD Loose Coupling Simulation

This paper presents the aeroacoustic analysis of a lift-offset coaxial rotor in high-speed forward flight using the high-fidelity computational fluid dynamics/computational structural dynamics (CFD/CSD) loose coupling software Helios. Acoustic simulations are performed using the software PSU-WOPWOP at eight microphones positioned below the coaxial rotor. The total power of the three speed cases—100, 150, and 200 kt—is validated against flight-test data and shows good agreement. A series of parametric studies is also conducted to investigate the effect of lift offset, flight speed, and rotor-to-rotor separation distance on acoustics of the coaxial rotor. Strong blade-crossover and self-blade–vortex interaction events of the coaxial rotor, which are major sources of loading noise, are captured via high-fidelity CFD simulations in all speed cases. Highly impulsive acoustic pressure signals are identified in all simulation cases, and the magnitude of mid-frequency sound pressure level (SPL) increases significantly with increasing flight speed and lift offset. The strength of mid-frequency SPL, on the other hand, is reduced significantly as the rotor-to-rotor separation distance increases at 100 kt. However, the higher speed cases do not show a significant reduction in mid-frequency SPL with increasing separation distance.

From Aeroacoustics Basic Research to a Modern Low-Noise Rotor Blade

In 2015, Airbus Helicopters unveiled the secrecy around its Dauphin successor and presented the all new H160 helicopter. A special feature that immediately attracted attention was its unusual and revolutionary fore-aft swept main rotor blade. This design, which aims to significantly reduce the blade-vortex interaction noise signature and reduce high-speed forward flight power requirements, was first investigated in the 1990s. At this time, DLR and ONERA formed a joint team to acoustically optimize a rectangular reference rotor blade. Based on state-of-the-art comprehensive rotor codes and a 50/50 work share, the ERATO rotor blade design was developed, patented worldwide and tested on both a rotor test rig and in the wind tunnel. Airbus Helicopters (then: Eurocopter) adopted the design, optimized hover and forward flight high lift performance and prepared it for serial production, as the Blue EdgeTM rotor blade on the Airbus Helicopters H160 helicopter.

Minimum Induced Power for a Rotor with a Finite Number of Blades

A dynamic inflow model is used to calculate minimum induced power for a helicopter in high-speed forward flight with a finite number of blades. Comparisons between analytical and numerical results are shown, and they show good agreement. Different flow conditions (such as with and without reverse flow or inflow feedback) are used to show how each condition affects optimum induced power. Several results confirm the findings of earlier investigations, such as a singularity in rotor power in reverse flow and induced power reduction with an increase in blade number. One of the new findings is that the induced power is affected by rotor solidity (in the absence of inflow feedback) and the effect of inflow feedback does not always reduce the induced power. Results obtained using higher harmonic blade pitch control show that induced power can thereby be reduced for all conditions with a finite number of blades.