Prediction and Measurement of Hovering Flapping Frequency Under Simulated Low-Air-Density and Low-Gravity Conditions

The ability to predict lift is crucial for enabling flapping flights on planets with varying air densities and gravities. After determining the lift required for a flapping flight on Earth, it can be predicted under different conditions using a scaling equation as a function of air density and gravity, assuming the cycle-average lift coefficient remains constant. However, in flapping wings, passive deformation due to aerodynamic and inertial forces may alter the flapping-wing kinematics, complicating predictions. In this study, we investigated changes in the lift coefficient of flapping wings under various air density and gravity conditions simulated using a low-pressure chamber and tilting stand, respectively. The current study found that the cycle-averaged lift coefficients remained nearly constant, varying by less than 7% across the air density and gravity conditions. The difference between the measured and predicted hovering frequencies increased under a lower air density due to the higher vibration-induced friction. The power consumption analysis demonstrated higher energy demands in thinner atmospheres and predicted a required power of 5.14 W for a hovering flight on Mars, which is a 66% increase compared to that on Earth. Future experiments will test Martian air density and gravity conditions to enable flapping flights on Mars.