We present an unsteady blade element theory (BET) model to estimate the aerodynamic forces produced by a freely flying beetle and a beetle-mimicking flapping wing system. Added mass and rotational forces are included to accommodate the unsteady force. In addition to the aerodynamic forces needed to accurately estimate the time history of the forces, the inertial forces of the wings are also calculated. All of the force components are considered based on the full three-dimensional (3D) motion of the wing. The result obtained by the present BET model is validated with the data which were presented in a reference paper. The difference between the averages of the estimated forces (lift and drag) and the measured forces in the reference is about 5.7%. The BET model is also used to estimate the force produced by a freely flying beetle and a beetle-mimicking flapping wing system. The wing kinematics used in the BET calculation of a real beetle and the flapping wing system are captured using high-speed cameras. The results show that the average estimated vertical force of the beetle is reasonably close to the weight of the beetle, and the average estimated thrust of the beetle-mimicking flapping wing system is in good agreement with the measured value. Our results show that the unsteady lift and drag coefficients measured by Dickinson et al are still useful for relatively higher Reynolds number cases, and the proposed BET can be a good way to estimate the force produced by a flapping wing system.

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The tailless flapping-wing micro air vehicle (FW-MAV) is one of the most challenging problems in flapping-wing design due to its lack of tail for inherent flight stability. It must be designed in such a way that it can produce proper augmented control moments modulated by a closed-loop attitude controller for active stabilization. We propose a tailless FW-MAV with a wing stroke plane modulation mechanism, namely NUS-Roboticbird, which maneuvers by only using its flapping wings for both propulsion and attitude control. The flying vehicle has four wings comprised by two pairs, and each pair of wings and its stroke plane are driven by a motor and a servo, respectively. Attitude control moments of roll, pitch and yaw are generated by vectoring a pair of thrusts, which result from changing the flapping frequency (or motor speed) and wing stroke plane of the two pairs of wings. Free-flight tests show that the vehicle can climb and descend vertically (throttle control), fly sideways left and right (roll control), fly forwards and backwards (pitch control), rotate clockwise and counterclockwise (yaw control), hover in mid-air (active self-stabilization), and maneuver in the figureof-8 and fast forward/backward flight. These abilities are especially important for surveillance and autonomous flight in terms of obstacle avoidance in an indoor environment. Flight test data show that an effective mechanical control mechanism and control gains for attitude-controlled flights for roll, pitch and yaw are achieved, in particular, yaw control. Currently, the vehicle weighing 31 g and having a wingspan of 22 cm can perform fast forward flight at a speed of about 5 m s −1 (18 km h −1 ) and endure 3.5 min in flight with a useful payload of a 4.5 g onboard camera for surveillance.

We briefly summarized how to design and fabricate an insect-mimicking flapping-wing system and demonstrate how to implement inherent pitching stability for stable vertical takeoff. The effect of relative locations of the Center of Gravity (CG) and the mean Aerodynamic Center (AC) on vertical flight was theoretically examined through static force balance consideration. We conducted a series of vertical takeoff tests in which the location of the mean AC was determined using an unsteady Blade Element Theory (BET) previously developed by the authors. Sequential images were captured during the takeoff tests using a high-speed camera. The results demonstrated that inherent pitching stability for vertical takeoff can be achieved by controlling the relative position between the CG and the mean AC of the flapping system.

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