# Aerodynamics from Cursorial Running to Aerial Gliding for Avian Flight Evolution
## 5 Results and Discussion  
### Trajectories of a Basal Paravian Dinosaur from Cursorial Running to Aerial Gliding  
By substituting the mass and size parameters of _Anchiornis_[36] into Equation (7), we can analyze its displacement and trajectory. Assuming that the initial velocity in the horizontal direction was 5 m/s and the inclined angle of the mountainside was \(\theta=30^{\circ}\), we obtained the trajectories of _Anchiornis_, as shown in Figure 3a, as \(v_{2}\) changed from 0 to 12 m/s. When the speed of the upslope wind changed from 0 m/s to 6 m/s within this velocity range of airflow, there was almost no possibility for the creature to glide up to a tree on the mountain slope, as shown in Figure 3b. When the speed of the upslope wind changed from 8 to 12 m/s within this velocity range of airflow, the creature could glide up to the branch of a tree of 6-m height when its horizontal displacement was about 15 m on the mountainside, as shown in Figure 3c. The detailed calculation for different velocities is illustrated in Figures S3-S5. Now, assuming that the initial velocity in the horizontal direction was 5 m/s and the inclined angle was \(\theta=10^{\circ}\), we obtained the trajectories of _Anchiornis_, as shown in Figure 4a, as \(v_{2}\) changed from 0 to 12 m/s. When the speed of the upslope wind changed from 0 to 6 m/s within the velocity range of airflow, the creature could barely glide on the mountainside, as shown in Figure 4b. When the speed of the upslope wind changed from 8 to 12 m/s within this velocity range of airflow, the creature could glide up to a tree branch higher than 1.2 m when its horizontal displacement was about 8-9 meters on the mountainside, as represented by Figure 4c. The detailed calculation for different velocities is illustrated in Figures S6-S8. Now, assuming that the initial velocity in the horizontal direction was 5 m/s and the inclined angle was \(\mathbf{\theta}\) = 0\({}^{\circ}\), which corresponded to the case on the plain ground, we obtained the trajectories of _Anchiornis_, as shown in Figure 5a, as \(\mathbf{v_{2}}\) changed from 0 to 12 m/s. When the speed of the wind changed from 0 to 12 m/s within this velocity range of airflow, there was no possibility for the _Anchiornis_ to glide up to 0 to 0.0496 m\({}^{2}\). Substituting the possible mass and size parameters of dinosaurs from Table 1 into Equation (7), we can draw the conclusions that when the running speed of a cursorial dinosaur was from 5 to 8 m/s and the tilt angle of the mountainside \(\mathbf{\theta}\) was larger than 0\({}^{\circ}\) but less than 30\({}^{\circ}\), the dinosaur could be lifted to follow a certain trajectory, falling into an interval that covered a tree on the mountainside. Assuming that the initial velocity in the horizontal direction was 8 m/s and the inclined angle was \(\mathbf{\theta}\) = 0\({}^{\circ}\), which corresponded to the case on the plain ground, we obtained the trajectories, as shown in Figure 5a for _Anchiornis_, as \(\mathbf{v_{2}}\) changed from 0 to 12 m/s. When the speed of the wind changed from 0 to 6 m/s within this velocity range of airflow, there was no possibility for _Anchiornis_ to glide up to any tree, as shown in Figure 6b. When the speed of the wind changed from 8 to 12 m/s within this velocity range of airflow, there was the possibility for _Anchiornis_ to glide up to 3 m.  
The above analysis is based on _Anchiornis_; therefore, similar conclusions can be drawn when we consider the mass parameters of other paravian dinosaurs, including _Epidexipteryx_[37], _Micronator_[38], _Archaeopteryx_[39], and _Confucisornis_[40], as summarized in Table 1. These dinosaurs are within the range from 0.11 kg to 1.5 kg, and the effective area parameters are within the range from 0.0132 m\({}^{2}\) to 0.0496 m\({}^{2}\).