Thrust Embedded 6DOF Modeling and Experimentation for Handling Fixed Wing Micro Aerial Vehicle Flight Instabilities

Abstract

A Flying Wing Micro Aerial Vehicle (FWMAV) flight characterization and model ing associated with propeller thrust has been worked upon. Reflexed airfoil selection methodology, static wind tunnel testing to investigate propeller induced flow effects on low aspect ratio wings and a computational estimation of longitudinal dynamic deriva tives has been carried out. FWMAV was fabricated using computer controlled hot wire machine with EPP (Expanded polypropylene) Styrofoam of density 50 Kg/m3 . Static aerodynamic coefficients were evaluated using wind tunnel tests conducted at cruise velocity of 20 m/s at varying angles of attack. Wind tunnel pyramidal balance calibra tion, experimental uncertainty assessment and corrections on the measured data was carried out. After static tests, wind tunnel experiments were carried out with rotating propellers. Three fixed pitch propeller diameters (5 inch, 6 inch and 7 inch), three pro peller rotational speeds (7800, 10800 and 12300 RPMs) and three wind tunnel speeds (10, 15 and 20 m/s) were considered to form up 27 advance ratios upon which wind tunnel testing was conducted. Left turning tendency of right-handed propellers was quantified in a form of newly proposed aerodynamic coefficients, which determined the change in aerodynamic coefficient with the change in advance ratio, J. Consequently six aerodynamic coefficients (CLJ , CDJ , CY J , CmJ , CnJ and ClJ ) were proposed and quantified. Damping effect in longitudinal flight mode is governed by the pitch dynamic deriva tives which are categorized into pitch rate derivative (Cmq), rotary derivative (Cmq˙), acceleration derivative (Cmα˙) and combined derivative (Cmq + Cmα˙). In this research a commercial software (Ansys®) was used to estimate pitch rate and pitch acceler ation derivatives of a FWMAV for correct estimation of dynamic effects. A steady pull-up maneuver with four constant pitch rates (2 deg/sec, 3 deg/sec, 4 deg/sec, and 5 deg/sec) was simulated to evaluate Cmq. Quasi Steady analysis using Single Rotating Frame (SRF) was employed to rvaluate pitch rate derivative Cmq. However simple harmonic motion (SHM) around mean angle of attack of 0◦ with amplitude of oscillation of ±3 ◦ was computationally simulated to estimate combined derivative (Cmq + Cmα˙) at four reduced frequencies (0.02, 0.03, 0.04, and 0.05) using unsteady simulation framework of Multiple Rotating Frame (MRF). After evaluation of aero dynamic derivatives in terms of static, rate and acceleration derivatives along with control derivatives in terms of advance ratio (J) derivatives and Elevon Control Power (ECP), a non-linear coupled 6-DoF mathematical model encompassing translational and rotational accelerations has been developed. A novel solution methodology for the estimation of dimensional derivatives is proposed and compared with the conventional Linear Time-Invariant Systems approach of available literature. Free response in terms of natural frequency, damping ratio, and time constant as well as forced response in terms of a unit step and a unit impulse elevon input has been calculated and analyzed. A noticeable variation in lift force, drag force, yawing moment and rolling moment against angle of attack was observed at low advance ratios J = V ωD , which indicated their significance at high propeller rotational speeds and large propeller diameters. Aerodynamic key performance parameter L D at trim point was found to be a nonlinear function of propeller diameter to wingspan ratio D b , and propeller rotational speed, ω. Further it was found that propeller induced flow has a significant contribution in flight dynamic modeling of low aspect ratio vehicles with large propeller diameter to wingspan ratio, D b of 22% or more. For tailless aerial platforms where no physical mechanism of time lag of wing vortices and their interaction with horizontal tail can be ascertained, the acceleration derivative Cmα˙ , can exist and provide necessary aug mentation in the pitch damping. The proposed solution methodology based on state space formulation predicted two pairs of complex conjugates for the longitudinal flight up to a pitch angle of 89◦ whereas conventional methodology predicted the same up to 57◦ . During flight trails, FWMAV was found to sustain straight and level flight without any flight controller or feedback control mechanism. However, higher natural frequencies of Phugoid and Short Period modes were observed upon pilot input or atmospheric gusts of around 1 m s . These high frequencies are conceived to be related to low mass Moment Of Inertia (MOI) and large magnitude of Zα Uo and Zu Uo . Finally, proposed solution methodology presented a more realistic representation of longitudi nal flight modes of FWMAV as compared to conventional methodology in existence today.