*7.2. Estimations of Perceived Gust for Fixed-Wing*

Now we consider the flight path of a fixed-wing UAV above the building roof as indicated in Figure 12 at representative speeds of 5 m/s and 15 m/s. Consider how the combined effects of flow angle and magnitude are perceived along one flight path by superimposing the vehicle flight speed *VV* onto the vertical speed *Vvert* and horizontal speed *Vhoriz* of the wind, *Vvert* and *Vhoriz* being the Cartesian analog of the "polar" results given in Figure 13. The superposition of the flight velocity and wind speed enables the relative velocity and angle of attack to be computed. The effective angle of attack, α(t), is calculated using

$$\alpha(t) = \alpha\_o + \operatorname{atan}\left(\frac{V\_{\text{vert}}}{V\_V + V\_{\text{horiz}}}\right) \tag{7}$$

The results for two nominal cruise speeds (5 m/s and 15 m/s), converted back into velocity magnitude and angle of attack, are given in Figure 15. The immediately obvious feature of Figure 15 occurs near the building leading edge, "0" of the abscissa. As expected from Figure 13, the shear layer atop the building results in the worst-case perceived gust encounter: at the lower flight velocity (5 ms−1) a ≈20◦ change in aircraft relative angle of attack is accompanied by an approximately 50% increase in velocity magnitude, all over a time increment of 0.25 s. At a higher flight velocity of 15 ms−1, the perceived angle of attack is lower (≈10◦), accompanied by a 25% increase in velocity over a time increment of 0.11 s. Using a simple linear relationship between the incident flow changes (angle of attack and relative velocity magnitude) and lift coefficient, and assuming a 2π lift curve slope and an unperturbed flight path (i.e., steady level flight), this gust represents changes in *CL* of 8.5 and 2 for a flight velocity of 5 ms−<sup>1</sup> and 15 ms−1, respectively. For flight paths at 45◦ (where one wing is immersed into the gust before the other) the roll moment coefficient *CLp* presented in Figure 15 is calculated from the lift imbalance between the aircraft's wings:

$$\mathbf{C}\_{L\_p} = \frac{b}{2} \ast \Delta \mathbf{C}\_L \tag{8}$$

$$\mathbb{C}\_{L\_p} = M / qSb \tag{9}$$

Taking time lags into consideration, conventional attitude sensing and control systems of a fixed wing UAV travelling at 10 ms−<sup>1</sup> will typically take 0.52 s to react (from sensing to actuation) [7,66] which can be insufficient to mitigate this gust. The combination of phase-advanced sensors, where flow, forward of the UAV, is measured and used as a control input [67], and novel control techniques may be needed [68] to achieve flight control in this type of environment. Examples of the latter include rotations of the entire wing, leadingedge control surfaces [68], or "fast flaps" at the trailing edge [69], which are intended to deflect faster than one convective time, producing lift transients well beyond what would be considered quasi-steady.

**Figure 15.** Gust shape as perceived by a moving aircraft. And the resultant *CL* in the vicinity of the rooftop (from a simple strip theory model, utilizing transient flow data). Note that position 0 denotes the physical edge of the building.
