# Structured Urban Airspace Capacity Analysis: Four Drone Delivery Cases
## 3 Flight Planning Algorithm
### Separation Concept in Route Network-Based Urban Airspace  
Conflict detection is activated when the separation of two sUASs is less than the minimum separation criterion. In this study, time-based separation is applied instead of the widely used distance-based separation to stabilise the spacing between all the sUASs. In this concept, a sUAS will occupy a waypoint when the sUAS passes the waypoint for a predetermined time interval. Within this time interval, no sUAS is allowed to traverse through the waypoint to satisfy the separation requirement. For each waypoint, a time interval list is maintained to keep track of the times at which the waypoint is expected to be occupied. These lists, called the flight schedule in this study, are shared between all sUASs during operation. By satisfying the separation assurance flight time at each waypoint rather than adjusting a distance between the sUASs, we can obtain results that satisfy the minimum separation along routes as well as at waypoints at all times. Note that, even if we consider homogeneous sUASs in this study, the separation concept can be applied to both heterogeneous and homogeneous cases. The separation concept allows time-based separation to be satisfied at merging points and crossing points as shown in Figures 3 and 4, respectively. At the time \(t_{0}\) of Figure 3, sUAS \(\alpha_{i}\) and sUAS \(\alpha_{i^{\prime}}\) fly towards the \(v_{\rm C}\) through the same merging point \(v_{\rm Y}\) at speeds  
Figure 2: A series of linear segments (sUAS \(\alpha_{i}\)’s flight route from its origin \(v_{1}^{j}\) to its destination \(v_{m_{i}}^{j}\)). \(s_{1}^{i}\) and \(s_{1}^{i^{\prime}}\), respectively. The time \(t_{0}\) is stored at each start point \(T(v_{\text{A}})\) and \(T(v_{\text{B}})\), and no sUAS can pass through both of the waypoints for separation time \(t_{SP}^{(i^{\prime},j)}\) seconds and \(t_{SP}^{(i^{\prime},j^{\prime})}\) seconds before and after \(t_{0}\), respectively. Note that, where \(t_{SP}^{(i^{\prime},j)}\) is dependent on the types of \(\alpha_{i}\) and \(\alpha_{i^{\prime}}\). The time \(t_{1}\) of Figure 3, when \(\alpha_{i^{\prime}}\) just passes through \(v_{\text{V}}\), is stored at the merging point \(T(v_{\text{Y}})\), and no sUAS can pass through this waypoint for \(t_{SP}^{(i^{\prime},j)}\) seconds before or after \(t_{1}\). The time \(t_{2}\) of Figure 3 is stored in \(T(v_{\text{Y}})\) in the same way. Then, \(\alpha_{i}\) and \(\alpha_{i^{\prime}}\) traverse towards \(v_{\text{C}}\) at speeds of \(s_{2}^{i}\) and \(s_{2}^{i^{\prime}}\), respectively. If \(\alpha_{i}\) and \(\alpha_{i^{\prime}}\) fly from \(v_{\text{M}}\) to \(v_{\text{C}}\) at speeds of \(s_{2}^{i}\) and \(s_{2}^{i^{\prime}}\), respectively, the separation between the two sUASs will always meet the separation requirement or be greater than that on the segment between \(v_{\text{Y}}\) and \(v_{\text{C}}\). At the time \(t_{3}\) of Figure 3, \(\alpha_{i}\) and \(\alpha_{i^{\prime}}\) fly at the same speed while maintaining the minimum separation. The flight schedule from \(t_{0}\) to \(t_{3}\) at each waypoint is as follows:  
\[T(v_{\text{A}}) =\{0s\},\] \[T(v_{\text{B}}) =\{0s\},\] \[T(v_{\text{Y}}) =\{0s,120s,210s\},\] \[T(v_{\text{C}}) =\emptyset.\]  
If no sUAS has passed waypoint \(v_{\text{C}}\), then \(T(v_{\text{C}})=\emptyset\). Such a flight schedule at each waypoint is used to formulate a flight planning problem that will be described in the following section. Note that, in this study we assume that all sUASs are of the same type to analyse the capacity with less decision parameters. Figure 3: Time-based separation concept for merging points. \(\alpha_{i}\) and \(\alpha_{i^{\prime}}\) are represented by superscript \(i\) and \(i^{\prime}\) in the figure, fly from their origin \(v_{\text{A}}\) and \(v_{\text{B}}\) to \(v_{\text{C}}\) through the merging point \(v_{\text{Y}}\) at speeds \(\{s_{1}^{i},s_{2}^{i}\}\) and \(\{s_{1}^{i^{\prime}},s_{2}^{i^{\prime}}\}\), respectively.