# Power Modeling and Experiment Study of Large Flapping-Wing Flying Robot during Forward Flight
## 4 Discussion  
To discuss the feasibility of the model, this section discusses the model and experimental results separately in detail and explains the reasons for the differences between the model and the experimental results. In Figure 9a,b, from the proposed model in this work, according to Equation (7), the total angle of attack \(\alpha\) of the wing strip increases as the static angle of attack \(\theta\) increases with the same wind speed and flapping frequency in the model, which results in an increase in the lift coefficient \(C_{n}(y)\) in Equation (15), where \(C_{n}(y)\) is positively associated with the overall angle of attack. This in turn leads to an increase in the induced drag coefficient \(C_{D,ind}\) from Equation (14) and the induced power \(P_{ind}\) in Equation (16). On the other hand, according to Equation (7), an increase in the static angle of attack \(\theta\) causes an increase in the induced velocity \(w\), which increases the induced drag power \(P_{ind}\). In addition, the  
Figure 10: (**a**) Power comparison of wing #1 with different velocity of wind and frequency in AOA = 5 m/s; (**b**) power comparison of wing #2 with different velocity of wind and frequency in AOA = 5 m/s; (**c**) power difference in percentage between the experimental and model result of wing #1; (**d**) power difference in percentage between the experimental and model result of wing #2.  
induced power is proportional to the velocity \(V\) in Equation (16) and the profile power is proportional to the cube of velocity \(V^{3}\) in Equation (18), so that the increase in velocity increased by flapping frequency causes an increase in power. Similarly, as the wind speed increases, the parasite power, which is proportional to the cube of horizontal velocity, increases as well, according to Equation (19), in addition to the induced power and profile power. This result is shown in Figure 10.  
In the experiments, the average power measured experimentally was obtained by controlling the FWAV to work at different wind speeds, different angles of attack, and different frequencies for the same time with the number of flapping cycles. The trend of the experimental results, together with the values, can be fitted with the model calculations, and increasing any of the conditions of wind speed, angle of attack, or frequency causes an increase in the average power consumption of the FWAV. However, there are discrepancies between the experimental results and the model when the flapping frequency is 1.5 Hz or the flapping frequency is larger than 3 Hz. In Figures 9c and 10c, the reason for the large difference between the average power calculated by the model and the average power measured experimentally at very low flapping frequencies comes mainly from the prototype platform. The brushless DC motor (SunnySky X2208) that we used is a motor that is mainly used in quadrotors. The alternating load applied to the motor is constantly changing as the wing flaps periodically, and the soft mechanical characteristics of such motors mean that motor has difficulty with constant speed output when the motor rotates at low speeds. The model assumes a constant speed output of the drive unit at 2\(\pi\)f; the angular velocity and angular acceleration in reality are smaller compared to the model when the motor rotates at low speeds, thus producing an obvious percentage difference at low speeds. Especially for wing #1, which has a larger wingspan and area than wing #2, it is more difficult for the motor to drive the wing #1 flapping at low speed, thus leading to the difference between the average power calculated by the model and the average power measured experimentally at 1.5 Hz flapping frequency, as shown in Figure 9a. In Figure 10d, the percentage difference is more significant when the flapping frequency is larger than 3.0 Hz. In Equation (2), to simplify the calculation, we simply set the maximum wing twist angle (which occurs at the wing tip) and the initial twist angle to 15\({}^{\circ}\) and 5\({}^{\circ}\), respectively.