*7.3. Estimations of Perceived Gust for a Rotor*

For multirotor aircraft, gust disturbances do not affect the aircraft in the same manner as fixed wing aircraft, especially in forward flight versus hover. This difference is due to the nature in which lift is created via its rotors and the forward motion flight state that requires a multirotor to tilt forward the rotors to generate forward speed. The purpose of this section is to explore the effect of the encountered gust on the total thrust generated while being agnostic about geometrical features of the rotor. This approach is key to making the analysis non-specific to a particular rotor and configuration but more generic and applicable to different multirotor configurations and even hybrid vehicles (i.e., fixed wing with rotors for Vertical Take-Off and Landing, VTOL). We will therefore use momentum disk theory and consider thrust of a single rotor. Aircraft designers can replicate this study and approximate the moments around the center of gravity for any number of rotors they intend to use. There are, however, limitations to this method, as it cannot account for geometric interferences between rotors and/or lifting surfaces, stall conditions, induced downwash effects from forward rotors, and other interactional aerodynamics of the configuration it may be modelling. However, it is sufficient for purposes of analyzing gust response within the context presented.

We consider two types of vehicles as outlined in Table 1 which represent two different scales of rotorcraft. The first vehicle represents a relatively small quadrotor delivery drone while the second is a larger octorotor AAM used for carrying human passengers. The tabulated specifications are generic for purposes of the presented analysis for two configurations which are likely to fly around buildings. The disk loading is determined by the hover weight divided by the total rotor area.


**Table 1.** Specifications of aircraft used for this analysis.

A single rotor disturbance model is used and is shown in Figure 16. Similar models have previously been used for turbulence and disturbance analysis for small multirotor aircraft with success [70,71].

The total induced thrust of the rotor can be represented b

$$T\_i = 2\rho A V v\_i \tag{10}$$

where the velocity components can be written as the induced velocity of the thrusting disk (*vi*), the wind velocity (*Vw*), and the summation of the two vectors resulting in total induced speed (*V*).

$$V = V\_w + v\_i \tag{11}$$

The wind disturbance model allows the oncoming wind vector to be separated into its horizontal and vertical components to resolve the total induced speed vector using

$$V = \sqrt{(V\_w \cos \alpha\_i + v\_i)^2 + (V\_w \sin \alpha\_i)^2} \tag{12}$$

where *αi* is the induced angle between the rotor disk and the relative oncoming wind vector. As induced angle is influenced by the rotor tilt angle (*φ*) required for forward flight, induced angle can be calculated using

$$
\alpha\_i = \pi/2 - \phi \tag{13}
$$

With no gust disturbance, the relative induced angle between the disk and the oncoming wind vector is completely perpendicular (*αi* = *π*/2). A purely vertical gust would result in a wind vector at zero or *π* radians with the thrusting vector parallel to the disk in hover. Vertical disturbances affect the angle of the disk relative to the oncoming wind vector, which allows oncoming gusts to approach the model between the angles of 0 ≤ *α<sup>i</sup>* ≤ *π*.

Tilt angles relative to the ongoing wind vector are calculated to be 34◦ and 63◦ using forward flight speeds of 5 ms−<sup>1</sup> and 15 ms−<sup>1</sup> by resolving the induced angle from Equation (12) assuming no wind gust disturbance. The upper flight velocity of 15 ms−<sup>1</sup> is regarded as high in terms of the normal flight speeds of multirotor aircraft at this scale; however, we offer this analysis to directly compare to the fixed wing case shown earlier. Referring to Figure 17, large variations are seen in the relative induced angle of the flow relative to the rotor. The most obvious effect can be seen at the buildings edge where larger variations of relative induced flow angle cause significant changes to thrust. The variation in thrust is more significant at the lower flight speed of 5 ms−1. The higher flight speed of 15 ms−<sup>1</sup> yields lower thrust variance due to a higher relative thrust required to maintaining flight and relatively lower gust vector. In other words, the faster the drone speed, the lower overall effect of the gust on the rotor as the thrusting vector to maintain flight becomes more dominant. Rotor thrust reactions to turbulence are more erratic and greater in magnitude than lift variations seen for the fixed wing aircraft found in the previous fixed wing study featured in this paper. On a rotor disk, turbulent flow vectors from all directions directly influence the aircraft incidence angle, the thrust required for steady level flight, and any perturbations which result in altitude loss or gain. All these directly influence the amount of thrust produced and incidence angle of the rotor significantly.

**Figure 17.** Gust shape as perceived by a moving thrusting disk of a delivery drone and the resultant effects on induced velocity, thrust, and normalized thrust in the vicinity of the rooftop. Note that position 0 denotes the physical leading edge of the building. *T/Th* is the thrust required over thrust to hover fraction.

The fixed wing aircraft seems to be more passively tolerant to turbulence (although further experimental studies are required to explore this). Lower tolerance of rotary wing is assumed to be due to the loss in forward flight of the disk when traversing though the gust resulting in increased power and induced velocity while inducing larger rotor tilt angles to maintain attitude and flight speed. As both lift and forward flight is maintained by propulsive means, large variations in power/thrust are required when each are influenced and have a compounding effect when traversing through a gust.

Flight altitudes closest to the building produce the most unsteadiness in rotary wing thrust variation, which is a direct result of the relatively thin shear layer producing a relatively sharp flow vector change. These effects near the building are consistent with the fixed wing aircraft in the previous analysis. We observe that upward gusts result in additional thrusting force required to maintain flight speed and altitude, which is clearly seen when the UAV experiences the large upward gust in Figure 17 at a normalized position between −0.4 and 0. The induced flow vector is altered in this region and results in a higher thrust production in the direction of flight. Flight altitudes of *h/H* = [0.0023, 0.047 and 0.14] demonstrate similar trends in thrust. All stabilizes when the disk traverses past the edge of the building to free stream flow which is upwind of the building. Flight altitudes of *h/H* = [0.25,0.33] involve flight through a less sharp gust as perceived by the UAV whereby less variations in thrust are observed. This is due to the UAV flying above the shear layer and recirculating flow area caused by the leading edge of the building, where only gradual changes in relative flow angle impinge on the disk. Unlike most fixed wing aircraft, multirotor aircraft are inherently unstable and rely heavily on stabilization through the variation of the thrust of each rotor. The response of the thrusting system (i.e., propellor, motor, and controller) is the limiting factor in correcting for disturbances. Slow-flying multirotor systems traversing through a building-induced gust will experience a relatively high magnitude of thrust variation and will thus require an active stabilization response to maintain steady level flight.

Figure 18 displays the same analysis presented in Figure 17 but for a larger AAM vehicle capable of carrying a human passenger, thus resulting in higher disk loading and thrust. Consequently, the vehicle is relatively less sensitive to the gust, whereby the induced velocity through the rotor, the overall thrust, and the non-dimensional thrust (*T/Th*) all show a lower thrust magnitude relative to the delivery drone. These changes are further highlighted in the non-dimensional thrust subplot where the maximum variance near the leading edge of building is Δ*T/Th* > 0.4, while the maximum variance for the delivery drone is greater at values of Δ*T/Th* > 0.8 at the same flight altitude and speed of 5 m/s. Variance in thrust magnitude is greater in all instances for the delivery drone relative to the urban mobility vehicle. In both flight examples, the variance occurs more so in the locations of highly separated and mixed flow featured at heights between 0.0023 < *h/H* < 0.14. Greater heights show smaller flow vector variation, suggesting regions of flow that are out of the turbulence shear layer. For both vehicles, the turbulence effects cannot be neglected and require active turbulence mitigation through autopilot stabilization. The suitability of stabilization systems depends on the actuation speed achievable for the given scale of the aircraft. Higher actuation speeds will reduce the sensing-to-actuation time-lag which thus enables the vehicle to mitigate sharper and higher-amplitude gusts. Light-weight rotors, high-torque motors, greater excess thrust, and power will all contribute to required turbulence reaction speeds.

**Figure 18.** Gust shape as perceived by a moving thrusting disk of an advanced air mobility vehicle, and the resultant effects on induced velocity, thrust, and normalized thrust in the vicinity of the rooftop. Note that position 0 denotes the physical edge of the building. *T/Th* is the thrust required over thrust to hover fraction.
