# A High-Fidelity Energy Efficient Path Planner for Unmanned Airships
## 6 Numerical Simulations
### Results and Discussion
The improvement in performance between the complete and the other planners was greater than the error in performance caused by the random gust wind component. Therefore, the inclusion of all three key factors to UAV trajectory planning yielded a significant improvement. Figure 10: Comparison of the average energy consumed per trial for each planner. The maximum computation time for a single trial of the complete planner was 78 s. It is worth noting that the WVFs were loaded from a calculated _a priori_ database. Hence, uploading variable WVFs' data using CFD computations in the physical UAV may lead to an additional overhead and so to a slight increase in the processing time. However, it was observed that the WVFs for these trials were calculated in 60 s, on average, and never more than 90 s using WindStation Version 4.0.1. The resulting total computation time to calculate the CFD WVF plus the trajectory over the 2 km \(\times\) 2 km \(\times\) 1 km control volume would still be only a fraction of the predicted flight time to traverse the trajectory. Since the trajectories can be planned faster than they can be followed, it is reasonable to conclude that the proposed complete trajectory planner could be used for unmanned airships. Depending on the desired resolution and on-board processing capabilities, it is foreseeable to include temporal and spatial WVF generation into the re-planning process or equipping the UAV with a local planner to find optimal paths within regions where obstacles are detected and re-planning is required, for instance. CFD-generated WVF data could also be fused with national weather vertice predictions (when available) and UAV-generated wind measurements for added certainty. The UAV attempts to arrive at the goal node within the allowed time frame by adjusting both the path in (4) and the vehicle speed in (5). This redundancy leads to a conservative trajectory planning approach. Based on the one-to-one weight ratio of time and energy, the ability to arrive at the goal node on time for the four respective planners was 53.2%, 53.2%, 87.2% and 91.5%, respectively. In addition, the complete planner arrived 32.5% earlier than expected, on average. If the weight for time is reduced, the arrival time will follow the goal time more closely. The average additional time due to reorientation of the UAV was on average 1.5% per convergent trial. Therefore, the idealized reorientation of Figure 3 is relevant to this UAV platform. The trajectory planner uses wind speed and direction to optimize the vehicle velocity and path. Therefore, incorporating turbulence intensity data into the path planner may further optimize the generated path. It is known that turbulence flows persist long into the wake of a disturbance. Although their intensity is low, it may have a detrimental effect on the flight performance. As an example, this means penalizing areas with relatively high turbulence intensities, such as the one circled in a solid line in Figure 10(a), and rewarding the others with low turbulence intensities, like the one circled in a dashed line. The CFD software WindStation, used to generate WVFs, also produces the turbulence intensity fields, shown in Figure 10(b). These data could readily be incorporated into the objectives in the cost function. However, platform-specific experimental flight data would be required to fully realize the impact of turbulence intensity on the flight performance and to properly utilize the turbulence data for trajectory planning. In addition to turbulence, thermal effects could also be included in the generation of the WVF generated by the CFD software to account for the vertical wind components produced by thermal convection [55]. Figure 11: Wind speed and turbulence intensity around a mountain ridge and city blocks. (**a**) Wind speed plot; (**b**) turbulence intensity plot.