# 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
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. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Species** & **Date (m. years)** & _Mass, m (Kg)_ & **Area, A (m2)** & **Figure of Fossil** \\ \hline _Epidecipteryx_ & 152-168 [37] & 0.164 [37] & 0.0132 [37] \\ \hline _Anchiornis_ & 155 [36] & 0.110 [37] & 0.04212 [36] \\ \hline _Archnaopteryx_ & 150 [38] & 0.276 [40] & 0.0496 [41] \\ \hline _Micronotor_ & 110-120 [42] & 1.50 [43] & 0.155 [21] \\ \hline _Cantiucisornis_ & 120 [40] & 0.500 [40] & 0.0402 [40] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Living era, mass, effective area, and fossil pictures of _Epidexipteryx_, _Anchiornis_, _Archaopteryx_, _Micronotor_, and _Conticisornis_. Theoretical analysis indicates that the meteorological conditions in the mountain and plain areas allowed the theropods to move from ground to trees. From the viewpoint of taking off from the ground, the velocity threshold is much lower than those predicted earlier [22]. Equation (6) indicates that the vertical component of the resultant force exerted on the dinosaur was dependent on the surface area of the body plane. Therefore, the longer and stronger the feather, the larger the area and the vertical component of the resultant force. So, glide activity propelled the development of the feathers of the bird's ancestors. The early ancestors of the bird could develop longer and longer feathers to adapt to the need for gliding activities. Therefore, the terrestrial theropods could easily benefit from the action of upslope winds in mountain areas or strong winds in plain grounds to get to the trees from the ground and again glide back to the ground. After calculating the speed of the upslope wind for different cases when the dinosaur was running at a speed from 5 to 8 m/s and the inclined angle \(\theta\) varied from 30\({}^{\circ}\) to 0\({}^{\circ}\) (Table 2), we obtained all the possible trajectories of _Epidexipteryx_ and _Anchiornis_ from ground to air. The trajectories of _Anchiornis_ were obtained for three cases when _Anchiornis_ was running at a speed of 5 m/s. Assuming that there is a tree at a distance of 10 m along \(x\)-direction, the value of \(v_{2}\) changes from 0 to 7.75 m/s, 7.75 to 9.35 m/s, and 9.35 to 11.20 m/s, for case 1, case 2, and case 3, respectively, as shown in Figure 7a. Similarly, the trajectories at a speed of 8 m/s can be obtained for _Anchiornis_ when \(v_{2}\) changes from 0 to 2.71 m/s, 2.71 to 5.85 m/s, and 5.85 to 9.83 m/s, respectively, for case 1, case 2, and case 3, as shown in Figure 7b. The same analysis is performed on _Epidexipteryx_ for all three cases at the speeds 5 m/s and 8 m/s, as shown in Figure 7c,d, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Species** & \(v_{1}\)(\(\frac{m}{s}\)) & \begin{tabular}{c} _Case_ 1 \\ \(v_{2}\)(\(\frac{m}{s}\)) \\ \end{tabular} & \
\begin{tabular}{c} _Case_ 2 \\ \(v_{2}\)(\(\frac{m}{s}\)) \\ \end{tabular} &
\begin{tabular}{c} _Case_ 3 \\ \(v_{2}\)(\(\frac{m}{s}\)) \\ \end{tabular} \\ \hline _Epidexipteryx_ & 5 & 0–7.75 & 7.75–9.35 & 9.35–11.20 \\ _Anchiornis_ & 5 & 0–7.75 & 7.75–9.35 & 9.35–11.20 \\ _Epidexipteryx_ & 8 & 0–2.71 & 2.71–5.85 & 5.85–9.83 \\ _Anchiornis_ & 8 & 0–2.71 & 2.71–5.85 & 5.85–9.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The speed of the upslope wind in different cases when the species ran at the speeds of 5 m/s and 8 m/s and the inclined angle was \(\theta\)=30\({}^{\circ}\). Figure 7: Trajectories of _Anchiornis_ running at a speed of: (**a**) 5 m/s; and (**b**) 8 m/s; Trajectories of _Epidexipteryx_ running at a speed of: (**c**) 5 m/s; and (**d**) 8 m/s.