# Drone Deployment Algorithms for Effective Communication Establishment in Disaster Affected Areas
## 3 Proposed Methods
### Region Filling
#### 3.4.3 Calculating Various Drone Parameters  
One of the prime considerations in drone deployment is that every drone should have the same leftover energy on deployment [18]. In this way, drones nearer to the base stations can be deployed at greater heights to cover the maximum area on the surface.  
We use drones with the same battery capacity and initial energy in the proposed method. After a drone is deployed, the leftover energy can be calculated as follows [18]:  
\[\begin{split}& e_{i}=B-C\times(dist_{i}+W\times(h_{i}-h_{b}))\\ & e_{i}=e_{j}\end{split} \tag{1}\]  
* \(W\)--the ratio of horizontal lift to drag ratio to vertical lift to drag ratio
* \(dist_{i}\)--the horizontal distance travelled by the \(i\)th drone  
One of our research objectives is to maximize the network coverage of the region. From Equation (1), the maximum leftover energy is obtained when \(dist_{i}=0\) and \(h_{i}=h_{max}\). Hence,  
\[e=B-C\times W(h_{max}-h_{b}) \tag{2}\]  
therefore, the maximum leftover energy is obtained when the drone is placed directly above the base station. From Equations (1) and (2), we obtain  
\[B-C\times W(h_{max}-h_{b}) =B-C\times(dist_{i}+W\times(h_{i}-h_{b}))\] \[\Rightarrow h_{i} =\frac{W\times H_{max}-dist_{i}}{W} \tag{3}\]  
Figure 6: An outline of the Region-Filling algorithm.  
For the first drone, \(dist_{1}=r_{1}\), where \(r_{1}\) is its radius of coverage. Because the coverage region is cone-shaped, \(r_{i}=h_{i}\times tana\); therefore,  
\[\begin{split} B-C\times W(h_{max}-h_{b})&=B-C\times (h_{1}\times tana+W\times(h_{1}-h_{b}))\\ \Rightarrow h_{1}&=\frac{W\times H_{max}}{W+tan\alpha} \end{split} \tag{4}\]  
The calculated height value \(h\) is adjusted to be within \(H_{min}\) and \(H_{max}\). The radius of coverage is calculated as  
\[r=h\times tan\,\alpha \tag{5}\]  
where \(\alpha\) is the coverage angle of the drone.  
Finally, in [18] the authors suggest an equation for finding the leftover energy \(e\) in one dimension:  
\[\begin{split} e&=B-C\times d_{i},\\ d_{i}&=|x_{i}-x_{i}^{\prime}|+W_{i}\times h_{i} \end{split} \tag{6}\]  
where \(B\) is the initial energy of the drone, \(C\) is the energy dissipation rate, and \(x_{i}\) and \(x_{i}^{\prime}\) are the positions of the base station and the drone, respectively. In our case, we have to consider both the Euclidean distance between the base station and the drone and the vertical distance that the drone has traveled (\(h-h_{b}\)). Hence, the above formula converges to  
\[e=B-C\times(dist+W\times(h-h_{b})) \tag{7}\]  
where \(h_{b}\) is the height of the base station. The height of a deployed drone and its coverage region are shown in Figure 7.  
In the above equation, the leftover energy is calculated following the assumption that the terrain is a plane. However, we use a threshold height \(H_{min}\) (defined in Section 3.3) for practical situations, below which the drone is not deployed. Obviously, this may not guarantee equal leftover energy for every drone, however, the average leftover energy for the entire system is greater than that for a system with drones deployed at equal heights. The procedure is described in Algorithm 1. Note that we fix the height of a drone to be the value of \(h_{fixed}\) (for the first two drones where \(h_{fixed}\
eq 0\)) in lines 11 and 12. Otherwise, we check whether the difference between the actual height (\(h+h_{ref}\)) computed for the drone and the height of the obstacle (\(h_{t}\)) is less than \(h_{td}\); if it is, we place the drone at a height \(h_{td}\) above the obstacle (line numbers 19 and 20).  
We try to cover the entire rectangular region with coverage circles of drones from the first base station to the second. We use a layered approach in which each layer consists of a starting circle, a set of circles along the \(x\)-direction, and a set of circles along the \(y\)-direction. The initial starting circle is placed near the base station at (0, 0).  
Figure 7: Visualization of a deployed drone and its coverage.