## 4 Test and Analysis  
### Lift and Voltage  
In the test the flapping the aircraft adopted PVDF and macromolecule polymer film as left and right wing respectively. Instead of lithium battery, DC voltage stabilizer was used to power the aircraft in case of instability induced by the consumption of battery electricity. A series of parametric tests were conducted for a range of flapping frequencies while keeping flapping wing platform driven motor input voltage constant in windless condition. The aerodynamic signal and voltage data were captured by load-cell and oscilloscope  
Figure 4: Photograph of the test system.  
Figure 5: The test system composition.  
Figure 6: Force measuring device and charge amplifier.  
respectively, stored on the computer. When the aircraft was excited, the load sensors were activated from idle condition to record the real-time value of the measured forces for about 60 continuous cycles.  
Figure 7 showed the variation of lift and voltage versus time at the 10 Hz flapping frequency based on a whole PVDF film without wet etching process. It appeared that the waveforms of these two kinds of data were very similar in waveform except for the amplitude size. It should be mentioned that except for the low flapping frequency phase, the lift and voltage curves always have good similarity in waveform. As a result, it provided the primary hypothesis that these two kinds of signal have certain relationship, then more experiments about PVDF wing were conducted.  
Combining the voltage data in Figure 7 and the Equation (16), we could get the root mean square (RMS) output voltage. The relationship of the mean lift force and RMS output voltage versus flapping frequency are shown in Figure 8. It can be seen from the fitting curves that the values of lift and voltage are proportional to the flapping frequency as the flapping frequency is below 14 Hz. Once flapping frequency exceeded the relative peak value, the payload and voltage value turned to a decreasing trend. This is because PVDF wing could not have enough time to finish the whole flapping motion in one cycle, which meant the PVDF wing was not able to accomplish the desired flapping amplitude. Due to complex deformation condition, it had a disturbance or counteraction phenomenon when the output signal had a different phase gradient of different bending the PVDF wing areas. These two factors collectively affected the increase trend of output voltage in high flapping frequency phase. As a result, it was important to choose an appropriate flapping frequency for PVDF wing application:  
\[U_{RMS}=\frac{1}{NT}\int_{0}^{NT}U^{2}(t)dt \tag{16}\]  
According to the varying trend of lift force and RMS voltage data in Figure 8, we could see that the voltage line lagged the payload line about 3 Hz and these two curves were very similar to each other in waveform without considering the phase shift between them. As a result, the functions over time of the force or voltage had a specific relationship and could be expressed by each other. It offered an opportunity to obtain the aerodynamic lift by measuring piezoelectric voltage signal for flapping aircrafts.  
Figure 7: Lift and voltage variation versus time at 10 Hz.