*7.1. Flight Trajectory Modelling*

Consider a UAV flying at speed *VV* in close proximity to a building. Depending on the flight path and the direction of the wind, a wide range of perturbations may be perceived (i.e., the gusts experienced relative to the moving UAV will vary with flight path and wind). Severe gusts are taken to be those that result in a large step change in aerodynamic forces or moments. Realizing that the atmospheric wind can vary from calm to extreme (i.e., storm) levels, it is necessary to select a single atmospheric wind speed and direction, then investigate flight paths relative to the building flow field that would generate the severe cases.

We consider the flight trajectories outlined in Figure 10, representing two flight paths towards the leading edge of the building (0◦ and 45◦ flight path angle), performed at some height above the rooftop, thus encountering the shear layers shed from the building structure. The 0◦ flight path represents the simpler case where the vehicle encounters the gust head-on, and there are no gust-induced rolling moments. The 45◦ flight path provides insight into the rolling moment that arises due to lift imbalance as one wing is immersed into the shear flow before the other wing. In reality, the UAV's trajectory will be influenced by the flow field. We ignore these vehicle dynamics and any coupling of the vehicle's flow field with that of the building and assume that the vehicle acts as a massless point-particle UAV. Thus, we assume "frozen" turbulence; that is, the computed wind field is sampled at one instant in time, and the "turbulence" encountered by the UAV is the variations in the relative flow field velocity as the vehicle proceeds in its idealized, steady level flight. While such simplification is unrealistic from the viewpoint of airplane flight mechanics, it is arguably sufficient to define a realistic "severe case" to be studied.

**Figure 10.** Planform view of flight paths considered in this paper.

The flow fields around a building were extracted from the CFD model (see Figure 11) to identify the gusts encountered as perceived by a moving aircraft. These flow fields were imposed on a simplified model of a fixed wing UAV in a way similar to that by Thompson, Watkins [60] as well as an actuation disk model of a single rotor, in order to extract severe cases during a straight flight path. The chosen aircraft speeds were 5 m/s and 15 m/s with respect to the ground (i.e., typical velocities for UAVs).

The flow extracted from the CFD simulation is presented in this section. The wind along a representative flight path (at fixed points along the flight trajectory) is shown in Figure 12. The flow field for various heights is depicted in Figure 13, and the flow extracted from the CFD simulation is given in Figure 14. The wind velocity is plotted as if it were in polar coordinates following the convention shown in Figure 12. The "flow pitch angle" is the direction of local flow at a *h/H* value of 0.0023 where *h* is the height of flight path above the rooftop and *H* is the building height. The trajectory closest to the roofline is at height ratio of *h/H* = 0.0023, or 10 cm above the roof, which is immersed in a boundary layer of the building itself. This boundary layer is present even at the intermediate trajectory height of *h/H* = 0.14, which is physically 6 m above the building. In this region, from 0 to <sup>−</sup>1 on the abscissa of Figure 13, the wind speed is low, but highly variable. At *h/H* = 0.25 and 0.33, the flight trajectory is above this building boundary layer and the flow pitch angle variation has settled down to a range within approximately 0–20◦. The normalized velocity is the wind speed magnitude normalized by the aforementioned 3 m/s reference velocity. If the wind field were uniform and parallel to the building roof, the flow pitch angle would be zero, and the "normalized velocity" would be a constant. Instead, there are

considerable variations in both angle and magnitude. The angle variations are not to be regarded as an angle of attack; at this point in the discussion, the airplane flight has not yet been introduced in the analysis. (Figures 13 and 14 represent the shape of the gust flow independent of the aircraft).

**Figure 11.** CFD domain, whereby air flows in the positive x-direction. The transient velocity magnitudes are shown in contour plots of the flow around the building located at the same plane of the flight paths (*travelling in the x-direction*) in the vicinity of the rooftop.

**Figure 12.** Encountered velocity vectors during proximity flight in the rooftop region of the building.

**Figure 13.** Flow velocity angles and magnitudes at different heights in the vicinity of the building's rooftop. Note that normalized positions −1 and 0 denote the edges of the building.

**Figure 14.** Velocity vectors along a representative flight path (*h/H* = 0.0023) in the rooftop region of the building as extracted from CFD simulation.

The changes in velocity magnitude are greatest very close to the building's top leading edge, whereas the changes in flow pitch angles are smaller. From the results presented in Figures 13 and 14, it is evident that a sharp increase in flow pitch angle at nondimensional position −1 on the abscissa exists at the trailing edge of the building. At the leading edge of the building, 0 on the abscissa, the flow pitch angle drops sharply. The normalized velocity, meanwhile, undergoes no change at the building trailing edge, but rises very sharply at the building leading edge. This rise is closer to the building leading edge for lower *h/H*, but it is essentially the same in magnitude for all trajectories up to *h/H* = 0.14 (6 m above the roof). This implies that a large change in wind amplitude is experienced by the UAV as it approaches the building edge, even if the desired trajectory is not particularly close to the building itself. In the presentation of Figure 13, wind speeds and angles are the result of the wind field computation, i.e., from a fixed reference frame. We next turn to how the very same results affect candidate UAVs of various kinds, i.e., from the UAVs' frame of reference.
