# Check-Valve Design in Enhancing Aerodynamic Performance of Flapping Wings
## 4 Discussion
### The Stability and Applicable Range of the Operation of the Check-Valve  
At high wind speed conditions, the drag increases sharply, especially when the upstream speed exceeds 2 m/s; the flapping motion is often forced to be interrupted. Regardless of whether there is a check-valve or not, when the inclined angle exceeds 50\({}^{\circ}\), there is no average lift and net thrust data. This provides an answer to the second question. At a high inclined angle, coupled with low wind speed, the inertia of the valve disc-cap does not change much because the high inclined angle of the wing is close to the vertical pull-up posture at the time of the upstroke. Therefore, it is believed that the valve may not work smoothly under the conditions of a high inclined angle coupled with low wind speed. During high wind speed (wind speed exceeding 2 m/s), with an inclined angle of less than 20\({}^{\circ}\), the instantaneous AOA will decrease. Due to this, the valve disc-cap will be directly impacted by the inlet flow and tend to return to the original position, and also closes the valve. The change in inertia of the valve disc-cap obviously opens the valve. The valve is generally open or closed, which makes the average lift and net thrust  
Figure 11: Concept design about the airflows on flapping wing surfaces with check valves: (a) air flow on the wing membrane with check-valve closing during downstroke, generating apparent positive lift; (b) flow separation due to check-valve opening during upstroke of an inclined wing, producing less negative lift; (c) flow separation due to check-valve opening during upstroke of a vertical wing, producing less positive lift. data measured by the wind tunnel severely fluctuate. The reliability of the data is also questioned. This explanation illustrates the third question, which also shows that the condition of high wind speed coupled with a small inclined angle is not suitable for the operation of check-valves. The aforementioned high inclined angle with low wind speed, and the high wind speed with small inclined angle are not applicable for check-valves. The only remaining proper application window is the medium wind speed range of 1.5-2.0 m/s and the inclined angle is close to 30\({}^{\circ}\). This coincides with the cruising conditions discussed in the previous section with the largest lift gain (by assigning the net thrust is zero), and it also helps to clarify the fourth question. The argument that the check-valve is opened due to inertia means that the radius of the valve disc-cap should not be too small (considering a 20 cm wingspan as an example, the disc-cap radius should be around 7 mm). In addition, it is known that the radius of the central orifice increases or decreases with the radius of the valve disc-cap. If the orifice is too small, it will also bring about the issue of low Reynolds number flow and high viscous fluid, so that the orifice cannot be passed through with airflow to affect the LEV and adjust the lift. The check-valve will completely malfunction. This explanation illustrates the fifth question. The inertia effect (gravitation) and the CFD are not considered in the previous modal and static analyses of FEA. If there is a more complete fluid-structure interaction (FSI) analysis tool in the future, it will fully include the effects from the valve disc-cap inertia, the aerodynamic lift/net thrust, and the supporting beam structure reaction force globally. It may be able to obtain a more satisfactory prediction of the simulation design. Additionally, regarding the worthiness of using check-valve design in the flapping wings, evaluating the flight power may be necessary. There are several ways to measure the power consumption of the FWMAV. One is to detect the electrical power, which includes the flight power, the friction loss of the flapping mechanism and the motor loss. Figuring out how to separate flight power from the total electrical power consumption requires a lengthy description.