Gusts Encountered by Flying Vehicles in Proximity to Buildings

Abstract

There is a growing desire to operate Uncrewed Air Vehicles (UAVs) in urban environments for parcel delivery, and passenger-carrying air taxis for Advanced Air Mobility (AAM). The turbulent flows and gusts around buildings and other urban infrastructure can affect the steadiness and stability of such air vehicles by generating a highly transient relative flow field. Our aim is to review existing gust models, then consider gust encounters in the vicinity of buildings as experienced by flight trajectories over the roof of a nominally cuboid building in a suburban atmospheric boundary layer. Simplified models of fixed- and rotary-wing aircraft are used to illustrate the changes in lift and thrust experienced by flight around the building. The analysis showed that fixed-wing aircraft experienced a substantial increase in angle of attack over a relatively short period of time (<1 s) as they fly through the shear layer at a representative forward velocity, which can be well above typical stall angles. Due to the slow flight speeds required for landing and take-off, significant control authority of rotor systems is required to ensure safe operation due to the high disturbance effects caused by localized gusts from buildings and protruding structures. Currently there appears to be negligible certification or regulation for AAM systems to ensure safe operations when traversing building flow fields under windy conditions and it is hoped that the insights provided in this paper will assist with future certification and regulation.

Full text

Citation: Mohamed, A.; Marino, M.;
Watkins, S.; Jaworski, J.; Jones, A.
Gusts Encountered by Flying
Vehicles in Proximity to Buildings.
Drones 2023,7, 22. https://doi.org/
10.3390/drones7010022
Academic Editors: Ivana Semanjski,
Antonio Pratelli, Massimiliano
Pieraccini, Silvio Semanjski,
Massimiliano Petri and
Sidharta Gautama
Received: 27 October 2022
Revised: 19 December 2022
Accepted: 23 December 2022
Published: 28 December 2022
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
drones
Article
Gusts Encountered by Flying Vehicles in Proximity to Buildings
Abdulghani Mohamed 1, * , Matthew Marino 1, Simon Watkins 1, Justin Jaworski 2and Anya Jones 3
1School of Engineering, RMIT University, Melbourne, VIC 3001, Australia
2Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
3Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
*Correspondence: abdulghani.mohamed@rmit.edu.au
Abstract:
There is a growing desire to operate Uncrewed Air Vehicles (UAVs) in urban environments
for parcel delivery, and passenger-carrying air taxis for Advanced Air Mobility (AAM). The turbulent
flows and gusts around buildings and other urban infrastructure can affect the steadiness and stability
of such air vehicles by generating a highly transient relative flow field. Our aim is to review existing
gust models, then consider gust encounters in the vicinity of buildings as experienced by flight
trajectories over the roof of a nominally cuboid building in a suburban atmospheric boundary layer.
Simplified models of fixed- and rotary-wing aircraft are used to illustrate the changes in lift and thrust
experienced by flight around the building. The analysis showed that fixed-wing aircraft experienced
a substantial increase in angle of attack over a relatively short period of time (<1 s) as they fly through
the shear layer at a representative forward velocity, which can be well above typical stall angles.
Due to the slow flight speeds required for landing and take-off, significant control authority of rotor
systems is required to ensure safe operation due to the high disturbance effects caused by localized
gusts from buildings and protruding structures. Currently there appears to be negligible certification
or regulation for AAM systems to ensure safe operations when traversing building flow fields under
windy conditions and it is hoped that the insights provided in this paper will assist with future
certification and regulation.
Keywords:
turbulence; gust; UAV; urban; severe; limitation; survey; CFD; city; urban air mobility;
buildings; infrastructure; air taxi; advanced air mobility; certification; regulation; vertiports
1. Background and Objectives
It is well documented that aircraft of all sizes are adversely affected by turbulence and
gusts; as identified by the Federal Aviation Administration (FAA) and the US Transportation
Safety Board as a leading cause of accidents—costing over USD 100M p.a. [
1
]. Severe
injuries are reported, such as those in the 2015 Air Canada flight AC088, which injured
21 passengers, including three children [
2
]; and 2019 Qantas Flight QF108 whereby 3 cabin
staff had head and neck injuries [
3
]. Accidents still continue to occur with more recent
accidents that resulted in injured passengers [
4
] and even a passenger death [
5
]. As the size,
mass and speed of aircraft decrease, the susceptibility to turbulence and gusts increases [
6
,
7
];
or in sum, due to lower wing loading [
8
]. Smaller general aviation aircraft and helicopters
also tend to fly more at lower altitudes within the Atmospheric Boundary Layer (ABL)
which is dominated by high turbulence intensities from ground protruding structures [
7
,
9
].
This has led to reported accidents directly relating to turbulence [
10
–
12
]. Even the transition
through the ABL can be detrimental to aircraft that are designed to fly at very high altitudes
such as Facebook’s Aquila Uncrewed Air Vehicle (UAV) and Airbus’ Zephyr UAV, whereby
both had fatal crashes due to turbulence and/or gusts [13,14].
The advent of Advanced Air Mobility (AAM) vehicles involves operating fleets of
UAVs in urban environments far more frequently than we have ever anticipated, for
the purpose of transporting parcels and passengers. This exposes the fleet of aircraft to
a wide range of challenging flow conditions; specifically large-scale gusts induced by
Drones 2023,7, 22. https://doi.org/10.3390/drones7010022 https://www.mdpi.com/journal/drones

Drones 2023,7, 22 2 of 25
urban infrastructure which can persist up to several kilometers away from the source
and interact in complex ways. AAM will more than often involve operation in close-
proximity to physical structures (e.g., inspection of infrastructure, or take-off and landing
operations from building rooftops). In the presence of large-scale gusts, significant flight
path deviations can occur, increasing risk of collision with objects. Aircraft collisions with
high-rise buildings is not unheard of [
15
], and the routine operation of UAVs in cities further
increases the risk of collisions. There is a need for both research and regulation efforts to
enhance safety and minimize the risk through considering vertiport and vehicular design.
The most relevant aspect of aviation to AAM, is the operation of helicopters which also
operate in urban environments albeit less frequently and with a human pilot onboard. From
a vehicular design standpoint, the AAM vehicles’ design and flight dynamics are different to
the conventional helicopter design which warrants an exploration into novel design features
and technologies that enable lower sensitivity to turbulence and precise maneuvering. From
a vertiport standpoint, the existing heliport infrastructure can potentially support AAM,
however there is a need for purpose-built buildings (for ease of public access and to
account for the autonomy of UAVs). The characterization of the flow field for a given wind
condition around heliports is limited in the literature and does not feature in any regulatory
framework for vertiport/heliport design. New research is thus required to characterize
the temporal and spatial variation in the flow fields around vertiports. This will inform
vertiport design and site selection, to minimize risk imposed by local wake of the building
from affecting flight safety.
In recent years, considerable attention has focused on measurements in ground-test
facilities or computations that replicate some idealized flow unsteadiness such as a pitching
and/or plunging maneuver or an imposed well-characterized gust [
16
–
23
]. However,
perhaps the most obvious gust problem for UAV flight is steady level operation, or at least,
intended steady level operation through the atmospheric boundary layer (ABL), where no
discrete obstacle (or associated wake) is present. Previous studies on UAV flight through
the ABL [
24
,
25
] have shown that three-dimensional (3-D) turbulent structures induce
particularly strong disturbances in UAV roll response owing to variation in effective angle
of attack along the wingspan. This disturbance in roll was also noted in comments from
pilots attempting to hold steady level flight in well-mixed turbulence [
26
]. Roll disturbances
not only degrade payload performance (particularly the blurring of images from optical
sensors) but may also lead to undesired flight path deviations. The most critical parts of
UAV urban operations entail flight in very close proximity to buildings and may include
entering buildings through windows or air vents or landing on their rooftops (see Figure 1).
Whilst the flow field around buildings has been extensively studied from a fixed reference
frame (e.g., by wind engineers for the purposes of structural loadings [
27
,
28
], dispersion
of pollutants [
29
,
30
], pedestrian wind comfort [
31
,
32
], etc.), there appear to be very few
studies from the reference frame of the moving aircraft and at the relevant frequencies [
33
].
We therefore examine this relative flow field with an overall aim to reveal the characteristics
of a “severe” gust for UAVs in close proximity to buildings.
In this paper we first review turbulence in the ABL to frame a taxonomy of gusts and
consider their relevance to UAVs. The more challenging flight environment for vehicles
passing through the local wakes of buildings is then considered and compared to flight
in the ABL. Flight in the urban environment is expected to yield gusts of high severity
(frequency and/or amplitude), most likely leading to unwanted, severe force spikes and
flow separation about the aircraft wing. While the problem is inherently 3D, we first
investigate a 2D longitudinal-only case by examining the relative flow near the centerplane
of the building. The outcome of this work is an assessment of the most basic research
question to characterize the urban environment: What are the disturbances in effective angle
of attack and relative flight speed magnitude in a flight-relevant urban gust encounter?

Drones 2023,7, 22 3 of 25
Drones 2023, 7, x FOR PEER REVIEW 3 of 26
a 2D longitudinal-only case by examining the relative flow near the centerplane of the
building. The outcome of this work is an assessment of the most basic research question
to characterize the urban environment: What are the disturbances in effective angle of
attack and relative flight speed magnitude in a flight-relevant urban gust encounter?
Figure 1. Notional flow field about a building generated by atmospheric winds.
2. Turbulence
Turbulence is defined as a chaotic, random, highly nonlinear and unpredictable flow
[34]. In the atmosphere, the characteristics of turbulence are influenced by the thermal
stability of the ABL (adiabatic, or various degrees of stability). However, under strong
winds mechanical mixing tends to dominate the turbulence generation mechanisms and
thermal stability plays a smaller role. Thus, in the current work we ignore thermally
driven turbulent flows, as they only tend to dominate under light winds, which are un-
likely to generate severe gusts. The ABL extends from the Earth’s surface up to an altitude
where the wind is no longer influenced by the roughness of the ground, which may in-
clude geological or civil structures. The mean wind speeds increase from zero at the
Earth’s surface up to the “gradient” wind speed, i.e., that which occurs at the gradient
height, typically 1–2 km depending upon terrain roughness. Above this height the air is
generally smooth, except for bursts of “clear air turbulence,” which are not considered
here. The ABL is well documented from stationary measurements for various purposes,
including meteorological and wind engineering studies (e.g., [35–37]). The interaction of
the ABL with obstacles such as buildings, bridges and other infrastructure will generate
coherent turbulence structures with length scales of a similar size to the obstacle, as de-
picted in a 3-D computational fluid dynamics (CFD) simulation shown in Figure 2, from
[38]. The building shown is nominally a cuboid of dimension 43 m, and the simulation
includes a representation of the velocity and intensity profiles in the approaching ABL.
Figure 3 further illustrates the decaying nature of turbulence in an urban scenario,
whereby the coherent structures dissipate downstream of obstacles, and a well-mixed tur-
bulent wake then develops (as can be seen downstream of the building in the figure).
These flow features yield a velocity field with a broad spectral content that contains a wide
range of length and time scales.
Figure 1. Notional flow field about a building generated by atmospheric winds.
2. Turbulence
Turbulence is defined as a chaotic, random, highly nonlinear and unpredictable
flow [
34
]. In the atmosphere, the characteristics of turbulence are influenced by the thermal
stability of the ABL (adiabatic, or various degrees of stability). However, under strong
winds mechanical mixing tends to dominate the turbulence generation mechanisms and
thermal stability plays a smaller role. Thus, in the current work we ignore thermally driven
turbulent flows, as they only tend to dominate under light winds, which are unlikely to
generate severe gusts. The ABL extends from the Earth’s surface up to an altitude where
the wind is no longer influenced by the roughness of the ground, which may include
geological or civil structures. The mean wind speeds increase from zero at the Earth’s
surface up to the “gradient” wind speed, i.e., that which occurs at the gradient height,
typically 1–2 km depending upon terrain roughness. Above this height the air is generally
smooth, except for bursts of “clear air turbulence,” which are not considered here. The
ABL is well documented from stationary measurements for various purposes, including
meteorological and wind engineering studies (e.g., [
35
–
37
]). The interaction of the ABL
with obstacles such as buildings, bridges and other infrastructure will generate coherent
turbulence structures with length scales of a similar size to the obstacle, as depicted in a
3-D computational fluid dynamics (CFD) simulation shown in Figure 2, from [
38
]. The
building shown is nominally a cuboid of dimension 43 m, and the simulation includes
a representation of the velocity and intensity profiles in the approaching ABL. Figure 3
further illustrates the decaying nature of turbulence in an urban scenario, whereby the
coherent structures dissipate downstream of obstacles, and a well-mixed turbulent wake
then develops (as can be seen downstream of the building in the figure). These flow features
yield a velocity field with a broad spectral content that contains a wide range of length and
time scales.

Drones 2023,7, 22 4 of 25
Drones 2023, 7, x FOR PEER REVIEW 4 of 26
Figure 2. Instantaneous velocities in the atmosphere in an urban environment. Flow travels from
left to right. With the reference height and velocity as U
∞
= 3 m/s and y
∞
= 10 m, this results in a
domain (average) Re of approximately 2.05 × 10
6
[38].
Figure 3. The atmospheric environment in an urban location.
3. Prior Gust Models
Aircraft encounter different types of turbulence while flying through the ABL, and
there exists a significant body of knowledge relevant to manned flight focused on the tem-
poral and spatial characteristics of the flow environment that is well-removed from local
effects and (usually) from the influence of the ground. These prior works include contin-
uous gust models that represent the structure of the statistically random flow fluctuations
in the atmosphere as power spectral functions. These spectra allow for predictions of the
mean-square values of the flight vehicle and aeroelastic responses, provided that a
Figure 2.
Instantaneous velocities in the atmosphere in an urban environment. Flow travels from
left to right. With the reference height and velocity as U
∞
= 3 m/s and y
∞
= 10 m, this results in a
domain (average) Re of approximately 2.05 ×106[38].
Drones 2023, 7, x FOR PEER REVIEW 4 of 26
Figure 2. Instantaneous velocities in the atmosphere in an urban environment. Flow travels from
left to right. With the reference height and velocity as U
∞
= 3 m/s and y
∞
= 10 m, this results in a
domain (average) Re of approximately 2.05 × 10
6
[38].
Figure 3. The atmospheric environment in an urban location.
3. Prior Gust Models
Aircraft encounter different types of turbulence while flying through the ABL, and
there exists a significant body of knowledge relevant to manned flight focused on the tem-
poral and spatial characteristics of the flow environment that is well-removed from local
effects and (usually) from the influence of the ground. These prior works include contin-
uous gust models that represent the structure of the statistically random flow fluctuations
in the atmosphere as power spectral functions. These spectra allow for predictions of the
mean-square values of the flight vehicle and aeroelastic responses, provided that a
Figure 3. The atmospheric environment in an urban location.
3. Prior Gust Models
Aircraft encounter different types of turbulence while flying through the ABL, and
there exists a significant body of knowledge relevant to manned flight focused on the
temporal and spatial characteristics of the flow environment that is well-removed from
local effects and (usually) from the influence of the ground. These prior works include
continuous gust models that represent the structure of the statistically random flow fluctu-
ations in the atmosphere as power spectral functions. These spectra allow for predictions
of the mean-square values of the flight vehicle and aeroelastic responses, provided that a

Drones 2023,7, 22 5 of 25
transfer function between the gust and response can be established from deterministic or
other means [39,40].
The most common continuous gust spectra of Von Karman [
41
], as well as those
of Diederich and Drischler [
42
], Dryden [
43
]) are one-dimensional, i.e., they yield three
orthogonal velocity components at a single point, a restriction that neglects gradients in
the gust across the aircraft as well as any altitude-dependent wind shear effects. These
gust models are built up from the statistical theory and measurements of isotropic turbu-
lence. The von Kármán model form interpolates between the isotropic scaling results of
Heisenberg [
44
] at low frequency and the higher-frequency scaling of Kolmogorov [
45
]
in the inertial subrange. The Dryden model instead assumes a functional form that fits
experimental measurements of the isotropic turbulent energy spectrum in the early stages
of decay; see Liepmann, Laufer [
46
] for further discussion and comparison of these gust
models. The choice of the simpler Dryden form over the more theoretically-grounded von
Kármán model is largely a matter of engineering convenience; the correctness advantage
of the von Kármán model is important only if significant spectral content relevant also to
the flight and aeroelastic dynamics is centered in the microscale range, a decade or more
above the integral scale break frequency where the isotropic inertial subrange begins [
47
].
The isotropic turbulence assumption, central to both models, is valid for turbulence at high
altitude. However, at lower altitudes relevant to UAVs/AAM (less than about 2000 ft),
anisotropic effects of the ABL without the influence of urban structures may be modeled
by adjusting the turbulence intensity and turbulence length scales in the isotropic models
according to empirical design specifications. Such specifications at low altitude for the von
Kármán and Dryden models, as well as a discussion of more sophisticated gust models, are
organized by Standard [
47
]. Continuous gust models may be compared with traditional
discrete gust models including the sharp-edged gust and “1-cosine” gust used to establish
severe aeroelastic scenarios. However, if desired, one may readily construct a continuous
gust from a known series of discrete gusts [
48
], and the continuous and discrete models
may be superposed provided that the flow disturbances and resulting structural motions
are sufficiently small to retain linearity.
Flows within an urban environment are generally inhomogeneous, anisotropic, and
time-varying and, therefore, violate many of the core assumptions of traditional gust
models. Near the ground, turbulence length scales and intensities vary rapidly with altitude
and depend strongly on the terrain [
49
]; there is a lack of viable models to describe the broad
range of general turbulent flows possible in this environment. The introduction of AAM
and UAVs further complicates the modelling challenge of the urban environment. Wind
shears from the terrain and from multi-scale arrays of buildings produce longitudinal and
vertical gusts that generate significant roll and yaw moments, which must be characterized
and accounted for in the gust and vehicle dynamics models [
50
]. In the absence of buildings
and terrain, the length scales of the most energetic eddies in the ABL are much larger than
the UAV feature lengths, and the high-frequency content of the turbulence spectrum is
therefore expected to play a more significant role in the vehicle gust response. However, the
urban landscape affects this turbulent flow and can introduce gust length scales pertinent
to the air vehicle response. Furthermore, the gusts encountered by UAVs near buildings
may be large relative to the local background flow and can lead to catastrophic nonlinear
effects, such as stall-induced pitch-up. In light of these challenges, the next sections
survey experimental measurements and computational simulations to characterize the
three-dimensional gust fields of canonical urban landscapes and investigate scenarios of
vehicle trajectories in this environment.

Drones 2023,7, 22 6 of 25
4. Turbulence Experienced by Moving Vehicles (Relative Turbulence)
Turbulence Intensity (Ti) is defined as the standard deviation of the fluctuating com-
ponent of wind velocity (u’) divided by the mean wind velocity (U),
Ti =q(u0)2
U=σ(u0)
U(1)
The variation in the intensities and scales with height from the ground from a station-
ary perspective (i.e., with reference to the ground) is described in Watkins, Thompson [
24
],
and a database compiled from a wide range of measurements can be found in ESDU
85020 [
51
]. Movement through the turbulence field at different speeds and directions
changes how the turbulence is perceived by moving vehicles. The effect of a moving mea-
surement reference frame has been explored by Watkins and Cooper [
52
] for ground-based
vehicles, where two-component data (in the horizontal plane) obtained from hot-wire
anemometers mounted above a vehicle were compared for fixed and moving vehicle frame-
works. Turbulence intensities measured from the moving vehicle were found to be in good
agreement with those predicted from the measured vehicle-fixed data in relatively smooth
domains, well-removed from local wakes such as buildings. However, when data were
obtained in rougher terrains, which included traversing local wakes, a significant increase
in turbulence intensity was found in the data from the moving vehicle. The lateral intensi-
ties were considerably higher than values predicted from ground-fixed data, whereas only
slight increases in longitudinal intensities were noted. This result was attributed to the fact
that turbulence from a stationary perspective (referenced to the ground) was measured at
locations specifically chosen to be removed from local wakes.
Watkins, Milbank [
6
] extended this work to include three-component data obtained
from four laterally spaced, dynamically calibrated, multi-hole Cobra probes. This extension
was carried out to understand the turbulent flow environment of UAVs, whereby the lateral
separation between the probes could be altered to document the flow impinging at different
spanwise locations on a UAV wing. Data were collected over various types of terrain,
and under a range of wind speeds and vehicle speeds that included some data closer to
buildings than in earlier hot-wire measurements. The closest that the measurement tracks
came to buildings was about 5 m due to the vehicle being driven on public roads. The
study provided data relating the measured turbulence intensities to relative flight velocity
(Figure 4), demonstrating a reduction with increasing freestream speed. In the moving
case, the denominator in the turbulence intensity (Equation (1)),
U
, becomes V
r
, which is
the vehicle speed relative to the air (i.e., the wind speed). Figure 5illustrates the vector
addition used to compute Vr,
Vr=qV2
w+V2
w−2VwVvcos θ(2)
It is therefore important to differentiate between Ti and the Relative Turbulence
Intensity (J), which takes into account the relative velocity, Vr:
J=qVW
02
Vr
=σVW
0
Vr
(3)

Drones 2023,7, 22 7 of 25
Drones 2023, 7, x FOR PEER REVIEW 7 of 26
Figure 4. The relationship between relative turbulence intensity J and flight velocity V
V
[6].
Figure 5. Aircraft and wind velocity vectors.
5. Relevant Gust Characteristics
Excessively large gusts (i.e., those with length scales significantly larger than the ve-
hicle’s characteristic dimension) can often be considered quasi-steady, and their effects
are relatively easily compensated for [6]. Gust scales equivalent to or smaller than the
characteristic length are more deleterious and introduce significant asymmetrical forces
and moments. As a gust impacts the leading edge of an aerodynamic surface such as a
wing, the flow angle and velocity are altered, inducing variations in the load distribution
as illustrated in Figure 6. Gusts of a 3-D nature that are smaller than the wing span will
lead to uneven lift distribution over the wings, inducing a rolling motion. Lissaman [53]
demonstrated that a sinusoidal load distribution with a period relating to a dimension
that is slightly larger than the span of the aircraft results in the maximum roll moment.
Gusts in well-mixed turbulence are highly three-dimensional in nature and it has
been shown that out of the possible six degrees of freedom, rolling motion is the most
significant disturbing factor for UAVs [6]. Atmospheric measurements in well-mixed tur-
bulence removed from building wakes illustrate the three-dimensionality of gusts,
whereby significant flow pitch variations are evident across typical UAV wingspans or
rotor diameters. Figure 7a shows a typical time record of the angle of attack, α, recorded
by four laterally separated probes during a two-second sampling time, showing large fluc-
tuations of the order of ±10°. At first, it might seem that there is a strong correlation be-
tween the pitch angles measured from the four probes. However, closer examination of
the data presented in Figure 7b reveals that there are considerable differences, and at some
instances the variation is ≈15° across probes with a lateral separation of 150 mm.
For fixed wings, Thompson, Watkins [54] showed that typical lateral variations in α
are more significant than the associated velocity magnitude variations in generating po-
tential rolling moments (using data from measurements of well-mixed atmospheric tur-
bulence close to the ground applied to simple wing strip theory). The experimental work
by Mohamed, Watkins [25] confirmed the high sensitivity of the roll axis to α variation.
Figure 4. The relationship between relative turbulence intensity Jand flight velocity VV[6].
Drones 2023, 7, x FOR PEER REVIEW 7 of 26
Figure 4. The relationship between relative turbulence intensity J and flight velocity V
V
[6].
Figure 5. Aircraft and wind velocity vectors.
5. Relevant Gust Characteristics
Excessively large gusts (i.e., those with length scales significantly larger than the ve-
hicle’s characteristic dimension) can often be considered quasi-steady, and their effects
are relatively easily compensated for [6]. Gust scales equivalent to or smaller than the
characteristic length are more deleterious and introduce significant asymmetrical forces
and moments. As a gust impacts the leading edge of an aerodynamic surface such as a
wing, the flow angle and velocity are altered, inducing variations in the load distribution
as illustrated in Figure 6. Gusts of a 3-D nature that are smaller than the wing span will
lead to uneven lift distribution over the wings, inducing a rolling motion. Lissaman [53]
demonstrated that a sinusoidal load distribution with a period relating to a dimension
that is slightly larger than the span of the aircraft results in the maximum roll moment.
Gusts in well-mixed turbulence are highly three-dimensional in nature and it has
been shown that out of the possible six degrees of freedom, rolling motion is the most
significant disturbing factor for UAVs [6]. Atmospheric measurements in well-mixed tur-
bulence removed from building wakes illustrate the three-dimensionality of gusts,
whereby significant flow pitch variations are evident across typical UAV wingspans or
rotor diameters. Figure 7a shows a typical time record of the angle of attack, α, recorded
by four laterally separated probes during a two-second sampling time, showing large fluc-
tuations of the order of ±10°. At first, it might seem that there is a strong correlation be-
tween the pitch angles measured from the four probes. However, closer examination of
the data presented in Figure 7b reveals that there are considerable differences, and at some
instances the variation is ≈15° across probes with a lateral separation of 150 mm.
For fixed wings, Thompson, Watkins [54] showed that typical lateral variations in α
are more significant than the associated velocity magnitude variations in generating po-
tential rolling moments (using data from measurements of well-mixed atmospheric tur-
bulence close to the ground applied to simple wing strip theory). The experimental work
by Mohamed, Watkins [25] confirmed the high sensitivity of the roll axis to α variation.
Figure 5. Aircraft and wind velocity vectors.
5. Relevant Gust Characteristics
Excessively large gusts (i.e., those with length scales significantly larger than the
vehicle’s characteristic dimension) can often be considered quasi-steady, and their effects
are relatively easily compensated for [
6
]. Gust scales equivalent to or smaller than the
characteristic length are more deleterious and introduce significant asymmetrical forces
and moments. As a gust impacts the leading edge of an aerodynamic surface such as a
wing, the flow angle and velocity are altered, inducing variations in the load distribution
as illustrated in Figure 6. Gusts of a 3-D nature that are smaller than the wing span will
lead to uneven lift distribution over the wings, inducing a rolling motion. Lissaman [
53
]
demonstrated that a sinusoidal load distribution with a period relating to a dimension that
is slightly larger than the span of the aircraft results in the maximum roll moment.
Drones 2023, 7, x FOR PEER REVIEW 8 of 26
For rotary wings, among the most relevant work was that conducted by Wang, Dai [55]
in which it was found that a variable pitch helicopter blade encountering a downward
gust experiences a significant reduction in thrust force. It was also found that the sharper
the gust, the more adverse the response is with respect to aerodynamic forces and struc-
tural deflection. This behavior is particularly relevant when travelling through shear lay-
ers at higher speeds, causing the relative encountered gust front to be perceived as a sharp
gust front.
Figure 6. Effect of gust length scale on wing loading. Adapted from Lissaman [53].
(a) (b)
Figure 7. Pitch angle variation: (a) 2-s sample (b) 0.2-s sample [6].
6. Gust Taxonomy
It is desirable to approximate gusts as quasi 1-D or 2-D (see Figure 8) for fundamental
studies on the transient flow field around airfoils through, for example, pitch and/or
plunge motions in fundamental experiments. However, the reality of well-mixed atmos-
pheric turbulence is intrinsically three-dimensional in nature. Discrete gusts can be cate-
gorized as either 1-D or 2-D in the streamwise or transverse directions. Streamwise 1D
gusts involve a momentary change in streamwise velocity. For example, as streamwise
velocity increases, the corresponding lift over an airfoil also increases, which if not cor-
rected, will result in a translation of the airfoil upwards (due to lift) and backwards (due
to the increased drag). Non-symmetric velocity changes along the span of a wing will
result in a rolling and yawing motion if not taken into consideration. It is worth noting
Figure 6. Effect of gust length scale on wing loading. Adapted from Lissaman [53].

Drones 2023,7, 22 8 of 25
Gusts in well-mixed turbulence are highly three-dimensional in nature and it has
been shown that out of the possible six degrees of freedom, rolling motion is the most
significant disturbing factor for UAVs [
6
]. Atmospheric measurements in well-mixed
turbulence removed from building wakes illustrate the three-dimensionality of gusts,
whereby significant flow pitch variations are evident across typical UAV wingspans or
rotor diameters. Figure 7a shows a typical time record of the angle of attack,
α
, recorded
by four laterally separated probes during a two-second sampling time, showing large
fluctuations of the order of
±
10
◦
. At first, it might seem that there is a strong correlation
between the pitch angles measured from the four probes. However, closer examination of
the data presented in Figure 7b reveals that there are considerable differences, and at some
instances the variation is ≈15◦across probes with a lateral separation of 150 mm.
Drones 2023, 7, x FOR PEER REVIEW 8 of 26
For rotary wings, among the most relevant work was that conducted by Wang, Dai [55]
in which it was found that a variable pitch helicopter blade encountering a downward
gust experiences a significant reduction in thrust force. It was also found that the sharper
the gust, the more adverse the response is with respect to aerodynamic forces and struc-
tural deflection. This behavior is particularly relevant when travelling through shear lay-
ers at higher speeds, causing the relative encountered gust front to be perceived as a sharp
gust front.
Figure 6. Effect of gust length scale on wing loading. Adapted from Lissaman [53].
(a) (b)
Figure 7. Pitch angle variation: (a) 2-s sample (b) 0.2-s sample [6].
6. Gust Taxonomy
It is desirable to approximate gusts as quasi 1-D or 2-D (see Figure 8) for fundamental
studies on the transient flow field around airfoils through, for example, pitch and/or
plunge motions in fundamental experiments. However, the reality of well-mixed atmos-
pheric turbulence is intrinsically three-dimensional in nature. Discrete gusts can be cate-
gorized as either 1-D or 2-D in the streamwise or transverse directions. Streamwise 1D
gusts involve a momentary change in streamwise velocity. For example, as streamwise
velocity increases, the corresponding lift over an airfoil also increases, which if not cor-
rected, will result in a translation of the airfoil upwards (due to lift) and backwards (due
to the increased drag). Non-symmetric velocity changes along the span of a wing will
result in a rolling and yawing motion if not taken into consideration. It is worth noting
Figure 7. Pitch angle variation: (a) 2-s sample (b) 0.2-s sample [6].
For fixed wings, Thompson, Watkins [
54
] showed that typical lateral variations in
α
are more significant than the associated velocity magnitude variations in generating
potential rolling moments (using data from measurements of well-mixed atmospheric
turbulence close to the ground applied to simple wing strip theory). The experimental
work by Mohamed, Watkins [
25
] confirmed the high sensitivity of the roll axis to
α
variation.
For rotary wings, among the most relevant work was that conducted by Wang, Dai [
55
] in
which it was found that a variable pitch helicopter blade encountering a downward gust
experiences a significant reduction in thrust force. It was also found that the sharper the
gust, the more adverse the response is with respect to aerodynamic forces and structural
deflection. This behavior is particularly relevant when travelling through shear layers
at higher speeds, causing the relative encountered gust front to be perceived as a sharp
gust front.
6. Gust Taxonomy
It is desirable to approximate gusts as quasi 1-D or 2-D (see Figure 8) for fundamental
studies on the transient flow field around airfoils through, for example, pitch and/or plunge
motions in fundamental experiments. However, the reality of well-mixed atmospheric
turbulence is intrinsically three-dimensional in nature. Discrete gusts can be categorized as
either 1-D or 2-D in the streamwise or transverse directions. Streamwise 1D gusts involve a
momentary change in streamwise velocity. For example, as streamwise velocity increases,
the corresponding lift over an airfoil also increases, which if not corrected, will result
in a translation of the airfoil upwards (due to lift) and backwards (due to the increased
drag). Non-symmetric velocity changes along the span of a wing will result in a rolling
and yawing motion if not taken into consideration. It is worth noting that Thompson,

Drones 2023,7, 22 9 of 25
Watkins [
54
], using a simple strip theory model, found that angular flow changes typically
have a tenfold greater effect on lift compared to the magnitude changes in atmospheric
turbulence. This behavior implies that travelling through a transverse gust will result in a
stronger generation of lift than from a streamwise gust.
Drones 2023, 7, x FOR PEER REVIEW 9 of 26
that Thompson, Watkins [54], using a simple strip theory model, found that angular flow
changes typically have a tenfold greater effect on lift compared to the magnitude changes
in atmospheric turbulence. This behavior implies that travelling through a transverse gust
will result in a stronger generation of lift than from a streamwise gust.
Figure 8. Dimensionality of gusts (modified from Diederich [56]).
7. Severe Gusts around Buildings: Case Studies
Let us now consider the flow field around a nominally cuboid building in a suburban
environment. At the juncture between the building and the ground plane, there is the
usual horseshoe vortex, perhaps with associated finer structures [57]. Near the building
rooftop, there is expected to be a separated flow with meandering shear layers of time-
varying position, width, and intensity. Depending on the building’s geometry and wind
direction, vortices may also be present near the rooftop. Using the taxonomy discussed in
the previous section, possible gust encounters by UAV flight in urban environments are
illustrated in Figure 9. Given that the angular flow changes typically have a greater effect
on sectional lift coefficient in contrast to magnitude changes [25], the most detrimental
case in this set is likely to be a transverse gust given the rapidity of the encounter with
respect to the flight trajectory. The latter scenario will therefore be the focus of a case study
presented in the remainder of this paper, whereby we use the flow field around a repre-
sentative cuboid building computed by Mohamed, Carrese [38] (see Figure 2) to estimate
variations in the lift and rolling moment coefficients of representative UAVs. The CFD
simulation representing an urban environment uses an Improved Delayed Detached
Eddy Simulation (IDDES) turbulence model. Mohamed, Carrese [38] validated the simu-
lation by demonstrating excellent agreement of the solution strategy with the experi-
mental and large eddy simulation (LES) data of similar but simpler cases. The validation
cases examined were: (1) developed channel flow, (2) flow over a backward-facing step,
(3) flow over periodic 2D hills, (4) wall-mounted hump flow, and (5) trailing-edge sepa-
ration over a hydrofoil. Full details of the basis of these simulations can be found in [38]
and comparison with point-probe atmospheric measurements is carried out in [33,58].
Figure 8. Dimensionality of gusts (modified from Diederich [56]).
7. Severe Gusts around Buildings: Case Studies
Let us now consider the flow field around a nominally cuboid building in a suburban
environment. At the juncture between the building and the ground plane, there is the
usual horseshoe vortex, perhaps with associated finer structures [
57
]. Near the building
rooftop, there is expected to be a separated flow with meandering shear layers of time-
varying position, width, and intensity. Depending on the building’s geometry and wind
direction, vortices may also be present near the rooftop. Using the taxonomy discussed in
the previous section, possible gust encounters by UAV flight in urban environments are
illustrated in Figure 9. Given that the angular flow changes typically have a greater effect
on sectional lift coefficient in contrast to magnitude changes [
25
], the most detrimental case
in this set is likely to be a transverse gust given the rapidity of the encounter with respect to
the flight trajectory. The latter scenario will therefore be the focus of a case study presented
in the remainder of this paper, whereby we use the flow field around a representative
cuboid building computed by Mohamed, Carrese [
38
] (see Figure 2) to estimate variations
in the lift and rolling moment coefficients of representative UAVs. The CFD simulation
representing an urban environment uses an Improved Delayed Detached Eddy Simulation
(IDDES) turbulence model. Mohamed, Carrese [
38
] validated the simulation by demon-
strating excellent agreement of the solution strategy with the experimental and large eddy
simulation (LES) data of similar but simpler cases. The validation cases examined were:
(1) developed channel flow, (2) flow over a backward-facing step, (3) flow over periodic
2D hills, (4) wall-mounted hump flow, and (5) trailing-edge separation over a hydrofoil.
Full details of the basis of these simulations can be found in [
38
] and comparison with
point-probe atmospheric measurements is carried out in [33,58].

Drones 2023,7, 22 10 of 25
Drones 2023, 7, x FOR PEER REVIEW 10 of 26
Figure 9. Schematics of possible gust encounters by a fixed wing UAV flying in the vicinity of build-
ings. Note drawn to scale for illustration purposes.
In the simulation, inflow boundary conditions replicate the relevant velocity and in-
tensity profiles of a suburban ABL. Due to the mesh resolution near the building (~0.05
m), the scales of the resolved turbulence are suitable for the UAV spans discussed in this
paper. Initialization of the IDDES simulation was provided using a steady-state k—ω SST
model. The RANS momentum field is converted to an instantaneous momentum field be-
fore commencing the transient run. The pressure-based Non-Iterative Time-Advancement
(NITA) fractional-step solver is utilized, with bounded second-order temporal discretiza-
tion. The time step is normalized by the ratio of (l
∞
/U
∞
) with a non-dimensional time-step
of ∆t∗ = 0.003 for the total time of the simulation t∗
T
= 600 with sampling statistics collected
from t∗ > 200. An average wind speed of 3 m/s at a height of 10 m was used in the upstream
boundary condition representing the ABL, and the mean wind direction was normal to
the southerly face (i.e., along the x-axis in the figures below). The modelling requirements
and profiles for the ABL were obtained from the work of Blocken, Stathopoulos [59], and
the ABL velocity profile U(y) was estimated using
𝑈(𝑦)=𝑢∗
𝜅.𝑙𝑛𝑦
𝑦0 (4)
where u* is the friction velocity, U
∞
and y
∞
are the reference velocity and height, κ is the
von Kármán constant, and y
0
is the equivalent aerodynamic roughness height. The profiles
for the turbulence kinetic energy k and specific dissipation ω were estimated using:
𝑘(𝑦)=𝑢∗2.𝐶0.5 (5)
𝜔(𝑦)= 𝑢∗.𝐶1.5.𝜅
𝑦 (6)
7.1. Flight Trajectory Modelling
Consider a UAV flying at speed V
V
in close proximity to a building. Depending on
the flight path and the direction of the wind, a wide range of perturbations may be per-
ceived (i.e., the gusts experienced relative to the moving UAV will vary with flight path
Figure 9.
Schematics of possible gust encounters by a fixed wing UAV flying in the vicinity of
buildings. Note drawn to scale for illustration purposes.
In the simulation, inflow boundary conditions replicate the relevant velocity and
intensity profiles of a suburban ABL. Due to the mesh resolution near the building (~0.05 m),
the scales of the resolved turbulence are suitable for the UAV spans discussed in this paper.
Initialization of the IDDES simulation was provided using a steady-state k—
ω
SST model.
The RANS momentum field is converted to an instantaneous momentum field before
commencing the transient run. The pressure-based Non-Iterative Time-Advancement
(NITA) fractional-step solver is utilized, with bounded second-order temporal discretization.
The time step is normalized by the ratio of (l
∞
/U
∞
) with a non-dimensional time-step of
∆
t
∗
= 0.003 for the total time of the simulation t
∗T
= 600 with sampling statistics collected from
t
∗
>200. An average wind speed of 3 m/s at a height of 10 m was used in the upstream
boundary condition representing the ABL, and the mean wind direction was normal to the
southerly face (i.e., along the x-axis in the figures below). The modelling requirements and
profiles for the ABL were obtained from the work of Blocken, Stathopoulos [
59
], and the
ABL velocity profile U(y) was estimated using
U(y) = u∗
κ·lny
y0(4)
where u* is the friction velocity, U
∞
and y
∞
are the reference velocity and height,
κ
is the
von Kármán constant, and y
0
is the equivalent aerodynamic roughness height. The profiles
for the turbulence kinetic energy kand specific dissipation ωwere estimated using:
k(y) = u∗2·Cµ−0.5 (5)
ω(y) = u∗·Cµ−1.5 ·κ
y(6)
7.1. Flight Trajectory Modelling
Consider a UAV flying at speed V
V
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

Drones 2023,7, 22 11 of 25
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.
Drones 2023, 7, x FOR PEER REVIEW 11 of 26
and wind). Severe gusts are taken to be those that result in a large step change in aerody-
namic forces or moments. Realizing that the atmospheric wind can vary from calm to ex-
treme (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 gen-
erate 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 struc-
ture. 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 influ-
enced by the flow field. We ignore these vehicle dynamics and any coupling of the vehi-
cle’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 [54] 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).
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 [
54
] 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 his the height of flight path
above the rooftop and His 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
−
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

Drones 2023,7, 22 12 of 25
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).
Drones 2023, 7, x FOR PEER REVIEW 12 of 26
Figure 11. CFD domain, whereby air flows in the positive x-direction. The transient velocity mag-
nitudes 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.
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 ex-
tracted 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 trajec-
tory height of h/H = 0.14, which is physically 6 m above the building. In this region, from
0 to −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.
Drones 2023, 7, x FOR PEER REVIEW 13 of 26
Figure 12. Encountered velocity vectors during proximity flight in the rooftop region of the build-
ing.
The changes in velocity magnitude are greatest very close to the building’s top lead-
ing 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 nondimen-
sional 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 particu-
larly 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.
Figure 12.
Encountered velocity vectors during proximity flight in the rooftop region of the building.

Drones 2023,7, 22 13 of 25
Drones 2022, 6, x FOR PEER REVIEW 14 of 26
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.
7.2. Estimations of Perceived Gust for Fixed-Wing
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.
Drones 2022, 6, x FOR PEER REVIEW 14 of 26
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.
7.2. Estimations of Perceived Gust for Fixed-Wing
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

Drones 2023,7, 22 14 of 25
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.
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 V
V
onto the vertical speed V
vert
and horizontal
speed V
horiz
of the wind, V
vert
and V
horiz
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
α(t) = αo+atanVvert
VV+Vhoriz (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 2
π
lift curve slope and
an unperturbed flight path (i.e., steady level flight), this gust represents changes in C
L
of
8.5 and 2 for a flight velocity of 5 ms
−1
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 C
Lp
presented in Figure 15 is calculated from the lift imbalance between the aircraft’s wings:
CLp=b
2∗∆CL(8)
CLp=M/qSb (9)
Taking time lags into consideration, conventional attitude sensing and control systems
of a fixed wing UAV travelling at 10 ms
−1
will typically take 0.52 s to react (from sensing
to actuation) [
7
,
60
] 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 [
61
], and novel control techniques may be needed [
62
] to achieve flight control in this
type of environment. Examples of the latter include rotations of the entire wing, leading-
edge control surfaces [
62
], or “fast flaps” at the trailing edge [
63
], which are intended to
deflect faster than one convective time, producing lift transients well beyond what would
be considered quasi-steady.

Drones 2023,7, 22 15 of 25
Drones 2022, 6, x FOR PEER REVIEW 16 of 26
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 de-
notes the physical edge of the building.
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 mak-
ing 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 ge-
ometric interferences between rotors and/or lifting surfaces, stall conditions, induced
downwash effects from forward rotors, and other interactional aerodynamics of the con-
figuration 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 Error! Reference source not found.
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 car-
rying human passengers. The tabulated specifications are generic for purposes of the pre-
sented 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.
Figure 15.
Gust shape as perceived by a moving aircraft. And the resultant C
L
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.
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.