## 3 Results  
Figures 4 and 5 show the probabilities of visual detection for drone flying with and without the protector, respectively. When the protector was used, the probabilities of visual detection for the \"definitely yes\" (DY) criterion were lower than those of the \"definitely or probably yes\" (DPY) criterion between the distance of 155 m and 452 m. Beyond 452 m, the probabilities of visual detection employing the two criteria coincided. The probabilities of visual catch for the DY criterion over all locations (0.29) was significantly (\(p<0.05\)) lower than that of the DPY criterion (0.47). When there  
was no detector, the probabilities of visual catch using the DY criterion were lower than those of the DPY criterion for all the distance. The probability of visual catch for the DY criterion averaged over all locations (0.29) was significantly (\(p<0.001\)) lower than that of the DPY criterion (0.44). The difference of the probabilities of visual catch between the two detector modes adopting the DY criterion was not significant. Neither was the difference of the probabilities of visual catch between the detector modes when the DPY criterion was adopted. We, then, focused our analysis on the visual catch data of the drone without the protector only. We conducted logistic regression analyses to predict the probability of visual capture versus the distance between the drone and the take-off spot. The dependent variables were \(P_{1}\) and \(P_{2}\). \(P_{1}\) and \(P_{2}\) are the probabilities of responding DY and DPY, respectively, for the drone hovering without the protector. The following equations were obtained:  
\[\text{Ln}(\frac{P1}{1-P1})=2.965-0.013\,\times\,\text{distance} \tag{2}\]  
\[\text{Ln}(\frac{P2}{1-P2})=4.292-0.014\,\times\,\text{distance} \tag{3}\]  
Figure 4: Probability of visual detection of the drone with the protector. Figure 5: Probability of visual detection of the drone without the protector. The coefficients of determination (or R\({}^{2}\)) of Equations (2) and (3) were 0.95 and 0.97, respectively. These equations may be rewritten as:  
\[P_{1}=\frac{e^{2.965-0.0132 distance}}{e^{2.965-0.0132 distance+1}} \tag{4}\]  
\[P_{2}=\frac{e^{4.292-0.0142 distance}}{e^{4.292-0.0142 distance+1}} \tag{5}\]  
Based on Equations (4) and (5), the estimated probabilities of visual detecting the Mavic Air drone flying without the protector were obtained (see Figure 6). The ratio of drone size (34.7 cm without protector) divided by the tangent of the visual angle was used to replace the distance in Equations (4) and (5). The predicted probabilities of visual capture versus the visual angle might, then, be obtained (see Figure 7). The predicted distances and visual angles for the LOS of the drone without the protector were calculated using Equations (4) and (5) (see Table 2). Investigating whether an operator can catch a drone in the air may be treated as a similar process of exploring the absol  
Figure 6: Estimated probability of visual detection. Figure 7: Probability of visual detection versus visual angle. detection. A probability of 50% has been adopted in finding out the threshold of the intensity of a stimulus [29]. The estimated drone distances for a 50% probability of visual catching employing the DY and DPY criteria for the Mavic Air flying without the protector, calculated using Equations (4) and (5), were 228 m and 307 m, respectively. The visual angles corresponding to these drone distances were 0.087\({}^{\circ}\) and 0.065\({}^{\circ}\), respectively. When the Mavic Air was flying with the protector, none of the participants could hear the sound of the drone when the horizontal distance was beyond 200 m at an altitude of 40 m AGL. When the drone was at 150 m away, only one participant out of 24 (1/24) heard the drone indistinctly and all others could not hear at all.