This paper presents a computational study on the free forward flight and sideslip manoeuvre of an insect-like flapping-wing flyer modelled after the hummingbird hawkmoth (Macroglossum stellatarum), with Reynolds number ${\sim}3000$ . The numerical model integrated a Navier–Stokes fluid solver with the Newtonian free-body dynamics of the flyer. A generic proportional–integral–derivative (PID)-based wing kinematics controller was used to achieve stable controlled flight. State-equation analyses of flight dynamics were helpful in identifying the roles of kinematic wing actions and for establishing control coefficients for stable flight. Forward flights up to a speed of $4.3~\text{m}~\text{s}^{-1}$ were simulated, which show that the wingbeat frequency decreased below the hovering frequency for cruising flight in the low- and medium-speed range, and higher frequency was only needed for high-speed flight. Similarly, the aerodynamic power consumption was also lower than that for hovering flight over the simulated speed range, due to the contribution of wing drag to overall lift. In addition, flight with higher speed tends to be more efficient in terms of energy consumption for the same distance travelled. In a complete sideslip manoeuvre, the model hawkmoth took approximately 20 wing cycles to translate laterally 4.5 wing lengths to its right and another 30 wing cycles to stabilize hovering at the new location. Slightly higher wingbeat frequency and power were required during the sideslipping phase to adjust for drop in lift due to body roll. The evolution of the vortical wakes reflects quite well the major mechanisms of force generation that were at play at key stages in these flights.

本文对以蜂鸟鹰蛾（Macroglossum stellatarum）为模型的昆虫状拍打翼飞行器的自由向前飞行和侧滑动作进行了计算研究，雷诺数为 $ {\ sim} 3000 $ 。数值模型将Navier–Stokes流体求解器与传单的牛顿自由动力学集成在一起。基于通用比例-积分-微分（PID）的机翼运动学控制器可实现稳定的受控飞行。飞行动力学的状态方程分析有助于确定运动机翼作用的作用，并有助于建立稳定飞行的控制系数。向前飞行，速度最高为 $ 4.3〜\ text {m}〜\ text {s} ^ {-1} $ 仿真结果表明，在低速和中速范围巡航飞行时，机翼频率降低到低于悬停频率，而高速飞行只需要较高的频率。同样，由于机翼阻力对总升力的贡献，空气动力消耗也低于在模拟速度范围内进行悬停飞行时的空气动力消耗。另外，就相同的行驶距离而言，在能量消耗方面，较高速度的飞行往往更有效。在完整的侧滑操纵中，鹰蛾模型需要大约20个机翼周期才能向右平移4.5个机翼长度，并需要另外30个机翼周期来稳定在新位置的悬停。在侧滑阶段需要稍高的机翼拍频率和功率，以调整由于身体侧倾而引起的升力下降。