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Unsteady Aerodynamic Parameter Estimation for Multirotor Helicopters*

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Unsteady Aerodynamic Parameter Estimation for Multirotor Helicopters* Trans. Japan Soc. Aero. Space Sci. Vol. 62, No. 1, pp. 32–40, 2019 DOI: 10.2322/tjsass.62.32 Unsteady Aerodynamic Parameter Estimation for Multirotor Helicopters* Hung Duc NGUYEN,† Yu LIU, and Koichi MORI Department of Aerospace Engineering, Nagoya University, Nagoya, Aichi 464–8603, Japan Today, multirotor helicopters (MRHs) play an important role in a broad range of applications such as transportation, observation and construction, and the safety of MRH flight is a matter of great concern. This study contributes to clarifying an aerodynamic aspect that enables the prediction of MRH behavior in unsteady conditions through flight tests. In working towards a comprehensive mathematical model that determines unsteady aerodynamics, a quadcopter is equipped with a data acquisition system to gather flight data including acceleration, angular rates, flow angles, airspeed and rotational speed. Based on the data collected, the combined blade element momentum theory is utilized to calculate steady and un- steady aerodynamic parameters. It is found that the experimental aerodynamic coefficients agree well with the theoretical results for steady forward flight. However, the conventional theory was insufficient to model the aerodynamic parameters under unsteady conditions. A new model to predict aerodynamic parameters under unsteady flight is proposed and vali- dated on the basis of the flight data. Key Words: Multirotor Helicopter, Unsteady Aerodynamics, Flight Experiment, Load Factor Nomenclature p: bias of roll rate q: bias of pitch rate a: 2-D lift curve slope r: bias of yaw rate ax: acceleration along xb axis x: bias of acceleration ax ay: acceleration along yb axis y: bias of acceleration ay az: acceleration along zb axis z: bias of acceleration az A: rotor disk area : advance ratio B: tip loss factor : air density c: blade chord : solidity CD: drag coefficient : roll angle CH: horizontal force coefficient : pitch angle CT: thrust coefficient avg: rotor average pitch angle h: altitude : yaw angle H: horizontal force !: rotational speed n: load factor Subscripts N: number of blades i: inertial frame p: roll rate exp: experiment q: pitch rate r: yaw rate 1. Introduction rl: fraction of blade span from axis (¼ l=R) R: rotor radius Today, multirotor helicopters (MRHs) play an important T: thrust role in a broad range of applications such as transportation, 1,2) u: translational velocity along xb axis observation and construction. For the safety of MRH v: translational velocity along yb axis flight, unsteady the aerodynamic response of MRHs to vi: induced velocity abrupt steering and/or wind gusts is a matter of great con- V: total velocity cern. V1: free-stream velocity In literature, a few studies have been devoted to MRH 3–5) w: translational velocity along zb axis aerodynamics. The interference of the front rotor on oper- : angle of attack ation of the rear rotor due to the wake generated by the front : sideslip angle rotor was examined in Hung et al.3) The effect of rotor blade : lock number flapping on attitude control was explored by Hoffmann et :inflow ratio al.4) A comparison of fixed and variable pitch actuators was presented through a series of experiments conducted © 2019 The Japan Society for Aeronautical and Space Sciences 5) + by Cutler et al. However, the unsteady aerodynamic charac- Received 18 September 2017; final revision received 16 June 2018; accepted for publication 17 July 2018. teristics of MRHs are still not completely understood. †Corresponding author, [email protected] Achieving a precise model of external forces acting on 32 Trans. Japan Soc. Aero. Space Sci., Vol. 62, No. 1, 2019 MRHs under maneuverable flight conditions leads to the re- element theory.8) In the momentum theory, the flow is as- quirement that considerable flight experiments need to be sumed to be incompressible and inviscid, and blade-loading carried out. In our previous study,3) a wind-tunnel was used is assumed to be distributed uniformly over the blade. The to investigate the steady aerodynamics of a quadrotor. How- blade element theory is based on the lifting-line assumption, ever, that was not sufficient. Unsteady conditions with time- neglecting stall.8) The advance ratio ®,inflow ratio ­, and varying parameters occur frequently in actual flight due to solidity · are defined as pilot operation and/or wind gusts. The load factor, n, has V1 cos been used conventionally to characterize the unsteady aero- ¼ ð1Þ !R dynamic load in structural design and maneuverable capabil- 6) ity of conventional helicopters. For safety when designing V1 sin þ vi ¼ ð2Þ the airframe and automatic control, it is indispensable to !R study the unsteady aerodynamic response of MRHs. Nc For this study, outdoor flight experiments were conducted ¼ : ð3Þ R to measure the aerodynamic forces and incoming flow vector using on-board sensors and a data acquisition system so that In the conventional theory, the thrust coefficient of a rotor unsteady aerodynamics could be examined. For investigating in forward flight with a linearly twisted pitch angle is 8) the aerodynamic characteristics of a quadrotor helicopter in ¼ 0 þ twrl, fl actual ight, this study addresses two primary interests: 1 1 1 1 fl fl C ¼ a B3 þ B4 þ B2 Steady forward ight and transition from forward ight to T 2 3 0 4 tw 2 0 ffi fl descent. Moreover, the thrust coe cient in transient ight ! ð4Þ is formulated as a function of the load factor, and is validated 1 1 þ B22 À B2 based on the experimental data collected. The methodology 4 tw 2 proposed will have a strong impact on the future studies of flight dynamics, flight simulation and adaptive control sys- or, constant twist, ¼ avg ! tem design of MRHs. 1 1 1 1 C ¼ a B3 þ B2 À B2 ð5Þ T 2 3 avg 2 avg 2 2. Mathematical Model and thrust, 2.1. Coordinate system T ¼ C !RðÞ24R2: ð6Þ It is necessary to define the different coordinate systems T for the following reasons7): The thrust coefficient based on the momentum theory is6): pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : Aerodynamic forces act on a quadrotor, such as the drag 2 2 ð7Þ CT ¼ 2ðÞ À tan þ : force described in the wind axes system and the thrust force described in the body axes system. By equating the right-hand sides of Eqs. (5) and (7), the : On-board sensors such as accelerometers and gyroscopes formula of the inflow ratio can be derived as: measure acceleration and angular rates with respect to ! 2 1 1 the sensory axes system. ¼ B3 þ B2 fi B2 3 avg 2 avg The coordinate systems are de ned as: Body axes system, ð8Þ Oxbybzb; wind axes system, Oxwywzw; and sensory axes sys- 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ox y z À ðÞ À tan 2 þ 2: tem, i i i; as shown in Fig. 1. B2a 2.2. Aerodynamic modeling for forward flight This model is based on the momentum theory and blade The Newton-Raphson procedure can be used to solve for ­ iteratively. The drag force can be split into three components: induced drag, profile drag and parasite drag. The horizontal force co- efficient is8): " ! C a 3 ÀÁ C ¼ d0 þ 0 À þ þ tw À þ H 4 2 3 1c 2 4 1c # ð9Þ 3 1 1 ÀÁ þ þ þ 2 þ 2 : 4 1c 6 0 1s 4 0 1c The first term in Eq. (9) is the profile drag and the second term is the induced drag. Different from most conventional helicopters, stifffixed- Fig. 1. Coordinate system definitions. pitch rotor blades are used on MRHs. In this study, a thin air- ©2019 JSASS 33 Trans. Japan Soc. Aero. Space Sci., Vol. 62, No. 1, 2019 Dexp foil is utilized and the approximate calculation of rotor blade Cexp ¼ total : ð20Þ flapping is based on the formula derived for helicopter rotor D !RðÞ24R2 blades9): "# 1 ÀÁ M It should be noted that Eqs. (5) and (15) are respectively ¼ 0:5 1 þ 2 À À w ð10Þ ffi ffi 0 2 4 3 I!2 theoretical thrust coe cient and drag coe cient in steady ! forward flight, whereas Eqs. (19) and (20) are respectively 4 experimental thrust coefficient and drag coefficient applied ¼ 2À ð11Þ 1c 3 0:5 for all flight regimes including hovering, forward, descent and transient flight. 4 ¼ ð12Þ 2.4. Unsteady aerodynamic parameter estimation using 1s 3 0 the recursive least squares (RLS) method 2 where, £ is the lock number, Mw ¼ mbladegR =2 is the mo- On the basis of Eq. (5), the thrust coefficient in steady for- 3 ment caused by the rotor blade and I ¼ mbladeR =3 is the in- ward flight can be written in polynomial form as the sum of ertia moment of the rotor blade. More precise calculations of the static term and derivatives of inflow ratio and advance ra- the flapping coefficients for stiff, fixed-pitch rotor blades tio as: were provided by Johnson.8) Then, the horizontal force H be- Cexp ¼ C þ C þ C 2: ð21Þ comes: T T0 T T2 By equating the right-hand sides of Eq. (5) and Eq. (21), H ¼ C !RðÞ24R2: ð13Þ H the expressions of parameters in steady forward flight are: The measurement of drag force is necessary to know the 1 maximum forward speed that the quadcopter can achieve C ¼ aB3 ð22Þ T0 6 avg for a specific angle of attack and rotational speed (RPM). For this purpose, the total drag force of the quadcopter is ex- 1 C ¼ aB2 ð23Þ pressed as: T 4 D ¼ T sin À H cos À D : ð14Þ 1 total parasite C ¼ aB : ð24Þ T2 4 avg The total drag coefficient of the quadcopter is finally for- mulated as: There are some aspects that should be noticed.
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