Sizing and Optimization of an Urban Air Mobility Aircraft Using Parametric Aero-Propulsive Model

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Sizing and Analysis of an Advanced Air Mobility Aircraft Using
Parametric Aero-Propulsive Model
Bikash Kunwar∗, Aashutosh Aman Mishra∗, Rajan Bhandari∗, and Imon Chakraborty†
Vehicle Systems, Dynamics, and Design Laboratory (VSDDL),
Department of Aerospace Engineering, Auburn University, Auburn, AL, USA
This paper presents the sizing and analysis of an inter-city advanced air mobility aircraft
using a semi-empirical parametric aero-propulsive model. The vehicle used in the analysis is a
tilt-wing configuration that can take off and land vertically like a rotary-wing aircraft and has
forward flight performance comparable to that of a fixed-wing concept. The aero-propulsive
model is first validated against an existing higher fidelity truth model, and then embedded
within the Parametric Energy-based Aircraft Configuration Evaluator sizing framework to size
the aircraft and study the effect of varying wing geometry parameters like wing loading, wing
aspect ratio, and wing taper ratio on overall vehicle sizing. The goal of this work is to integrate
a parametric aero-propulsive model into the sizing framework which will allow the designers to
have an initial estimate of the vehicle size and performance characteristics in the conceptual
design phase with minimum wait time.
I. Introduction
The
aircraft industry has seen notable growth of novel aircraft concepts that promise a change in the future of air
mobility [
1
–
11
]. These aircraft are electric or hybrid electric and are usually designed for vertical take-off and
landing (VTOL) [
1
–
4
,
6
–
10
] or short take-off and landing (STOL) [
5
] operations in addition to cruise. These aircraft
come in various forms, such as lift-plus-cruise [
2
], tilt-wing [
10
], and tilt-rotor [
1
,
3
,
4
], and exhibit complex flow
interactions and dynamic behavior. The interest in such unconventional aircraft concepts and accompanying complexity
has resulted in significant efforts to develop modern sizing and analysis tools. The shortcomings of traditional sizing
and analysis methods [
12
–
15
] become apparent when examining new configurations like this. These techniques
rely on weight fractions of mission segments obtained from historical data or computed using a limited range of
aerodynamic, propulsion, and flight condition parameters. Even more detailed approaches[
16
,
17
], which numerically
integrate aircraft performance and trajectory over smaller time intervals comprising discretized mission segments, may
also have limitations. There are a few limitations that need to be taken into account. These include the inability to
account for hovering, transitioning, and forward flight within the same framework, especially when mode transitions
are involved, as well as the lack of explicit trim analysis and consideration of rotational degrees of freedom. These
issues are particularly problematic when analyzing VTOL aircraft, where propulsors are used as control effectors,
and controllability requirements can have a significant impact on propulsion system power sizing. Additionally, the
typical separate representation of aerodynamic and propulsive characteristics can create issues for distributed propulsion
or boundary-layer ingestion scenarios. Also, the underlying setup assumptions aligned with either fixed-wing or
rotary-wing aircraft can create roadblocks for analyzing VTOL aircraft with characteristics of both.
Efforts to develop modern sizing and analysis tools have been made due to the increased interest in advanced
air mobility (AAM) and urban air mobility (UAM), with the aim of addressing some of the limitations mentioned
earlier. For instance, Brown and Harris used simplified aero-propulsive models to optimize various UAM aircraft
configurations based on trip cost [
18
]. Similarly, Kadhiresan and Duffy compared different UAM concepts and identified
the best-performing configurations based on weight-based optimization [
19
]. Silva et al. compared different UAM
concepts and demonstrated various technologies and design approaches[
20
]. Kraenzler et al. used the blade element
method to analyze the aero-propulsive characteristics of multirotor, LPC, and tilt-wing concepts with all-electric (AE)
propulsion [
21
]. Warren et al. explored how range and battery technology factors affected the sizing and performance of
e-VTOL aircraft [
22
]. Meanwhile, Hendricks et al. employed a multidisciplinary approach using the NASA OpenMDAO
framework to analyze a turbo-electric (TE) tilt-wing UAM design [
23
]. Finally, Hamilton and German and Bryson et
∗Graduate Student, VSDDL, Department of Aerospace Engineering, Auburn University, AIAA Student Member.
†Assistant Professor and VSDDL Director, Department of Aerospace Engineering, Auburn University, AIAA Associate Fellow.
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AIAA AVIATION 2023 Forum
12-16 June 2023, San Diego, CA and Online
10.2514/6.2023-3662
Copyright © 2023 by Bikash Kunwar, Aashutosh Aman Mishra, Rajan Bhandari, Imon Chakraborty.
Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
AIAA AVIATION Forum

al. analyzed the selection of optimal electric aircraft cruise speeds and found Pareto-optimal designs for small hybrid
unmanned aerial systems [24].
Many of the studies mentioned above share a common thread, which involves the adaptation or expansion of
conventional sizing techniques to accommodate new types of aircraft and propulsion systems. Similarly, the Parametric
Energy-based Aircraft Configuration Evaluator (PEACE) sizing framework was created with a broad scope in mind,
allowing for its general application to a wide range of aircraft and propulsion systems. Its salient features are explained
in Sec. II. The initial design phase of these aircraft involves characterizing the candidate configurations, exploring
alternatives, and performing design trade studies to arrive at the best candidate configuration from a pool of hundreds of
possible configurations. After the selection of the configuration, it is desired to perform sizing and optimization of the
aircraft as well as other studies such as structural analysis, flight dynamics analysis, and simulation. Design cycle time
can be significantly reduced by having a rapid-evaluation aero-propulsive analysis tool whose result can be carried over
to perform other design analyses. This paper uses a strip-theory-based approach to modeling lifting surfaces using
semi-empirical methods to perform the sizing of an advanced air mobility vehicle.
The standard aerodynamic analysis tools at the disposal of the designers are classical inviscid methods such as lifting
line theory and vortex lattice method (VLM), quasi-3D methods, and high-fidelity computational fluid dynamics (CFD)
[
25
]. The inviscid methods in their original or modified form are widely used to predict lifting surface aerodynamics.
Prandtl lifting line theory is used to analyze the aerodynamic performance of wings with relatively low aspect ratios.
Several studies propose various modifications on the Prandtl lifting line to account for non-linear effects [
26
–
30
] . The
Weissinger lifting line theory is one of the extensions of the Prandtl lifting line theory that accounts for nonlinear lift
distribution that can occur on wings with high aspect ratios. Weissinger’s non-linear lifting line, with only one chordwise
element, is considered the precursor to VLM where both a spanwise and chordwise distribution of horseshoe vortices
are placed on the wing. Despite this, the method can reasonably predict the aerodynamics for test cases involving
unswept, swept-back, and tapered wings with dihedral. With high sweep, in both forward and aft direction, there is an
increase in spanwise flow which causes a highly three-dimensional flow field which the method does not completely
capture. Philips and Snyder [
28
] developed a general numerical lifting-line method based on the Prandtl’s lifting line
to analyze the lifting surfaces with arbitrary camber, sweep, and dihedral. Gallay and Laurendeau [
30
] applied the
method to wing, high-lift systems (slat/ main/ control surface), and multisurface configurations. Computational Fluid
Dynamics (CFD) can accurately simulate turbulent flow but requires significant computational resources and time. In
contrast, classical methods like the Lifting-Line Theory (LLT) and Vortex Lattice Method (VLM) are computationally
less expensive, reducing the computation time by at least one order of magnitude compared to CFD solvers, but their
applicability is limited as they simplify the problem being studied with a set of assumptions.
There are also simple analytical approximation methods that may be used for the purpose of the initial design.
Schrenk [
31
] developed a method, now commonly known as Schrenk’s method, for rapidly computing the spanwise lift
distribution over a wing. This method assumes that the real lift distribution lies between the ideal (elliptic) distribution
independent of the wing shape and the distribution determined in a simple manner by the wing shape. For an untwisted
wing with some planform, for lift coefficient
𝐶𝐿=1
and dynamic pressure
𝑞=1
, the real lift distribution will be the
average of the elliptical and planform chord distributions. For a twisted wing, the real lift distribution is the sum of the
basic lift distribution (corresponding to wing
𝐶𝐿=0
) and additional lift distribution determined as if the wing was
untwisted [
32
]. The results of the method show satisfactory agreement with those calculated by the exact method by
solving the full set of Navier-Stokes equations. However, the simple method does not take into account the sweep of
the lifting surface in its calculation. In doing so, the simple method does not differentiate between the aerodynamic
properties of the same planform with different sweep angles. Moreover, the method does not provide a direct way to
determine induced drag and no way to determine the profile drag of the wing.
Recent studies have pursued the rapid computation of wing performance for sizing and optimization. A common
theme of these studies is using quasi-3D methods for aerodynamic model development and surrogate-based methods for
optimization. In a typical conventional industrial environment during multidisciplinary design optimization (MDO),
this method belongs to a level 1 fidelity. Level 3 using Reynolds-averaged Navier-Stokes (RANS) is the highest
fidelity method [
33
]. Marcus et al. [
34
] used the panel method to develop the wing aerodynamic model to analyze the
over-the-wing (OTW) propeller and wing performance in a cruise condition. This technique agreed well with the wind
tunnel results when the control surface was retracted. However, the tool gave unrealistic results when the control surface
was deflected, mainly due to the limitation of panel code in regions with significant viscous effects or recirculation.
Alba et al. [
35
] used VLM, 2-D airfoil data, simple sweep theory, and strip theory to develop an aerodynamic model
for surrogate-based optimization of general aviation aircraft with tractor propeller configuration. The result from the
aerodynamic model showed good agreement against the wind tunnel results.
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The common aerodynamic methods can be placed on a fidelity and computation cost spectrum, as shown in Fig. 1.
The application of Schrenk’s method will yield approximate results very quickly, and the use of high-fidelity RANS will
yield accurate results at the expense of computation cost. Iterative methods such as numerical lifting line, VLM, and
Fig. 1 Placement of studied aerodynamic method amongst other aerodynamic methods on computation cost
and fidelity spectrum
panel code with the integration of 2-D airfoil data fall under quasi-3D methods and work well for aerodynamic analysis.
But they require multiple iterations to converge to a solution which does not make them conducive to rapid sizing or
simulation studies where the aerodynamic model has to be solved numerous times. The fidelity of the surrogate models,
which are mathematical or statistical models trained using a set of input-output data generated from experiments, wind
tunnel tests, or computational fluid dynamics simulations, is less than the parent method providing input-output data,
but the computation cost is lower. The current method exploits the historical aircraft database, which is the result
of theoretical model and experiments, and uses a strip-theory based approach to yield relatively higher fidelity than
theoretical methods alone but at lesser computation time due to the very nature of the data and methods as the parameters
of aircraft geometry, states, and flight conditions. The data and methods are derived from aircraft design literature,
including USAF Stability and Control Data Compendium (DATCOM) [
36
], NASA technical reports[
37
,
38
]. The
available data, which are usually functions of concerned lifting surface parameters such as airfoil shape, geometry, and
operating conditions, are converted into one or higher dimension look-up table, from which appropriate correlations
are constructed. This will result in a significant saving in pre-processing and computation time. For the purpose of
configuration selection, sizing, and optimization, these correlations need to be obtained only once and saved for future
usage. The aerodynamic model will be numerically coupled to propeller design tools: QMIL [
39
] and QPROP [
40
] to
make an aero-propulsive model inside the sizing framework called Parametric Energy-based Aircraft Configuration
Evaluator (PEACE) [41–46].
The work in this paper first develops an aerodynamic model of the lifting surfaces, control surfaces, and non-lifting
surfaces as described in section IV, and embeds inside PEACE described in section II. The result of the implementation
are then compared against those of commercial high-fidelity software FlightStream®to establish the validity of the
model in section V. These results establish the embedded model agrees well with the truth model as lifting surface
geometry is varied over the selected range. Then, the model is used to size and optimize an Advanced Air Mobility
(AAM) vehicle whose configuration is described in section III. The results of sizing are also presented in section V.
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II. Parametric Energy-based Aircraft Configuration Evaluator (PEACE)
PEACE is an aircraft sizing framework developed at VSDDL that can size aircraft with novel configurations and
conventional fixed-wing designs. This framework employs a generalized, energy-based formulation of flight vehicle
performance, not limited to conventional fixed or rotary-wing designs [
47
]. The generalization of propulsive power and
energy concepts enables equivalent sizing and analysis for conventional and electrified propulsion architectures. The
aircraft is not considered a point mass; the rotational degrees of freedom are considered by trimming the aircraft model
to calculate the power required or the available performance. This framework also employs a parametric geometry
representation of the aircraft and a set of resizing rules that govern the recalculation of component locations and
dimensions over successive sizing iterations. The overview of aircraft sizing and mission analysis using PEACE is
shown in Figure 2. The framework is set up to analyze the desired aircraft concept through the following:
1)
Aero-propulsive performance model (APPM): The APPM outlines how the aircraft’s net aerodynamic reaction
is developed. It can include static lookup tables, reduced order models, embedded strip theory or blade element
momentum theory-based analyses, or a mix of these.
2)
Weight estimation relationships (WER): These consist of a combination of empirical/historical weight
relationships for aircraft components or incorporated physics-based calculations for other component weights.
3)
Geometry parameterization: The definition of the notional aircraft concept in terms of how the main parts are
arranged relative to one another, producing parametric geometry that is later scaled and sized. This definition
includes, among other things, the attachment of lifting surfaces to nacelles and to fuselages.
4)
Geometry update rules: These rules control how the aircraft geometry changes as the sizing iterations occur.
Simple examples include mounting a propulsor at a specific normalized spanwise location on a lifting surface
and sizing a wing or rotor to maintain a desired wing loading or disc loading, respectively.
The inputs to the framework are the following:
1)
Technology state-of-the-art (SOTA): Power-to-mass ratios, specific energy, efficiencies, and other functional
relationships can all be used to specify the SOTA for components of propulsion architecture.
2)
Point performance constraints: To determine the required power ratings for propulsion system components,
Fig. 2 Overview of PEACE vehicle sizing and mission analysis framework
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point performance constraints are assessed under either nominal or off-nominal (degraded) operating conditions.
3) Payload: The payload can be specified for both design and off-design missions.
4)
Mission profile: The design and off-design mission profiles can be specified as a series of mission segments that
fall into one of three categories: vertical flight mode (VFM), forward flight mode (FFM), or transition.
5)
End-of-mission energy constraints: These can be specified as a fixed amount of energy, a percentage of starting
energy (e.g., a battery’s minimum end-of-mission state-of-charge), or a percentage of used energy.
6)
Maximum takeoff mass (MTOM) starting guess: This guess is required to start the first iteration of sizing.
The PEACE framework iteratively varies MTOM to meet mission energy requirements in subsequent iterations.
The Vehicle/System Updater uses the current iteration MTOM (or, for the first iteration, the MTOM guess) to
perform several functions in order to size the aircraft:
•
Geometry Updater: Based on the parametric geometry definition and geometry update rules, this module
computes and updates the aircraft’s geometry. Downstream modules make use of the updated geometry definition.
•Power Sizer: This module trims the aircraft at a specified amount of nominal and off-nominal (degraded) flight
conditions and evaluates the relevant power flow equations to determine the power outputs of each component in
the propulsion system architecture. This reveals the nominal or off-nominal scenarios for calculating the required
power of various propulsion system architecture components.
•
Component and Empty Mass Calculator: Based on the WERs and the SOTA technology, this module computes
the masses of structural components, systems, and propulsion system components. The total of these masses
equals the aircraft’s empty mass.
•
Energy Mass Calculator: The computed empty mass and given payload are subtracted from MTOM to calculate
the start-of-mission energy mass. If multiple energy sources are available, the energy mass is distributed according
to the utilization ratio determined by mission analysis. An equal split is used for the first iteration (prior to mission
analysis).
•
CG and Inertia Calculator: This module computes component CG and inertia based on the masses and geometry
determined by previous modules. To obtain aircraft CG, the component CGs are mass-averaged. Component
inertias are transformed from component centroidal axes to aircraft body axes, shifted from the component CG to
the aircraft reference point (via the parallel axis theorem), and finally summed to obtain aircraft inertias.
•
Mission Analyzer: This module computes the trajectory time history, as well as the time variation of mass and
propulsive energy over each mission segment, by evaluating them sequentially and passing information between
them. Each segment is discretized into a number of points, at which the aircraft is trimmed explicitly. The power
flow model of its propulsion system is then evaluated to determine the rate of energy consumption and rate of
mass change. The end-of-mission energy is determined once all segments have been evaluated.
•
Mass/Energy Converger: The converger calculates the excess energy mass (EEM) by subtracting the end-of-
mission energy for each energy source from the minimum value allowed by end-of-mission energy constraints and
converting these energy differences into equivalent masses using the specific energies of each energy source. The
EEM contains as many elements as there are energy sources. A positive value for an EEM element indicates
an excess of that type of energy, whereas a negative value indicates a deficit. The converger’s goal is to achieve
energy balance by iteratively varying MTOM until each EEM element is individually driven to zero (in practical
terms, below a specified tolerance) by one of the methods listed below:
1)
Method 1: The next iteration’s MTOM change is calculated as
Δ
MTOM =
−(Δ
MTOM
/Δ
EEM
)×
EEM.
For the first iteration, the ratio
(Δ
MTOM
/Δ
EEM) is set to a fixed value, and subsequent iterations are
computed based on the MTOM and EEM iteration histories.
2)
Method 2: The MTOM for the next iteration is updated (respectively, decreased or increased) by relatively
large increments based on the sign of EEM in a given iteration (i.e., excess or deficit) until EEM has
opposite signs between two successive iterations. This creates an MTOM interval around the solution. To
converge around the MTOM solution, the interval is then halved using the bisection algorithm.
3)
Method 3: This is a combination of Methods 1 and 2. The iterations begin with Method 2, in order to
bracket the solution and quickly reduce the interval. Once the energy mass fraction (ratio of total energy
mass to MTOM) has stabilized to within a pre-set tolerance or the interval is smaller than a specified
threshold, the solution method switches to Method 1 until final convergence.
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Off-design missions for a sized vehicle can be analyzed in Analysis mode (rather than Sizing mode), in which the
Vehicle/System Updater is not executed, and the takeoff mass is calculated by adding empty mass, payload mass, and
starting energy mass. A mission parameter, such as the range of a main cruise segment, is updated iteratively until
end-of-mission energy requirements are met. The payload-range characteristics of the sized aircraft are determined by
evaluating such off-design missions with varying payload and energy combinations.
The aircraft geometry definition in PEACE can be used directly with the embedded aero-propulsive model, as is done
in this study. It can also be exported to AC3D [
48
] file format (.ac), which can then be imported into FlightStream®[
49
]
for aero-propulsive model development or flight simulation programs (e.g., X-Plane [50] or FlightGear [51]).
A. Aero-Propulsive Performance Model (APPM)
Fig. 3 Input/output functional form of the APPM
The APPM’s input/output functional form is depicted in Fig. 3and is independent of vehicle configuration and
propulsion system architecture. The APPM inputs are divided into two groups: (i) parameters that can change within a
sizing iteration based on flight conditions, and (ii) parameters that can change between sizing iterations but remain
constant within an iteration. The input parameters falling under the first category are:
•
Angle of attack,
𝛼
: This is the angle formed by the longitudinal axis of the vehicle and its velocity vector. The
angle of attack is defined to be zero in hover conditions, where this definition fails.
•
Flightpath angle,
𝛾
: The angle formed by the velocity vector and the horizontal. It is used to resolve buoyant
and gravity forces along wind axes, and it is related to velocity
𝑉
and vertical velocity
𝑑ℎ/𝑑𝑡
by the equation
𝑑ℎ/𝑑𝑡 =𝑉sin 𝛾.
•
Control vector,
𝛿𝑐=𝛿𝑐1, 𝛿𝑐2, . . . , 𝛿𝑐𝑛
: The control vector’s elements describe the vehicle’s control effector
states. The number of control effectors modeled by the APPM varies depending on the configuration.
•
Control allocation: This is a rule-set mapping the control vector elements to a smaller number of control variables
for over-actuated configurations where the number of control effectors exceeds the number of degrees of freedom.
•
Throttle vector,
𝛿𝑡=𝛿𝑡1, 𝛿𝑡2, . . . , 𝛿𝑡𝑝
: Normalized parameters
𝛿𝑡𝑖∈ [0,1]
that can be mapped to propeller
RPM, blade pitch, or shaft power input, or throttle setting for gas turbines. The term ”throttle” is used somewhat
loosely to indicate that increasing
𝛿𝑡𝑖
should correspond to increasing propulsive power output from the propulsor
at a given flight condition. The number of throttle parameters is determined by the propulsion architecture.
•
Propulsion mode: This is used to specify the current mode of operation for propulsion system architectures that
have multiple operating modes (e.g., a power mode and a recharge mode).
•
Flight condition,
{𝜌(ℎ), 𝑉∞, 𝑀∞, . . .}
: These parameters define freestream conditions for flight in standard or
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non-standard atmospheres, and they have a significant impact on aero-propulsive characteristics and propulsor
performance.
The parameters in the second category, which can change between sizing iterations but are constant within them, are:
•
Aero-propulsive model: This may comprise lookup tables expressing the aerodynamic and propulsor reactions as
functions of flight condition and other parameters, the embedded execution of other analysis scripts that determine
the above, or a combination thereof. The model itself may update between iterations as the vehicle resizes.
•
Propulsion and energy systems SOTA: The specific fuel consumption or fuel flow model of fuel-burning
propulsion systems, as well as the efficiencies or efficiency models of propulsion system components, are included
in the SOTA definition. As the vehicle resizes, these characteristics may change between iterations.
•
Power flow model(s): The power flow model contains relationships that govern the flow of power from energy
sources to propulsion system components to propulsors along each power path. When a propulsion system has
multiple operating modes, multiple power flow models may exist.
The outputs from the APPM are:
•
Aerodynamic reactions,
𝐹𝑥𝐴, 𝐹𝑧𝐴, 𝑀𝑦𝐴
: The combined effects of aero-propulsive and buoyant forces. They in-
clude axial and normal forces in wind axes (
𝐹𝑥𝐴, 𝐹𝑧𝐴
) and pitching, rolling, and yawing moments (
𝑀𝑦𝐴, 𝑀𝑥𝐴, 𝑀𝑧𝐴
).
•
Rate of change of energy source masses,
𝑑𝑚
𝑑𝑡 =n𝑑𝑚1
𝑑𝑡 ,𝑑𝑚2
𝑑𝑡 , . . .o
: For fuel-burning propulsion systems, the
mass rate of change is negative, zero for electric propulsion, and can be positive for certain fuel cell chemistries.
•
Rate of change of energy contents,
𝑑𝐸
𝑑𝑡 =n𝑑 𝐸1
𝑑𝑡 ,𝑑 𝐸2
𝑑𝑡 , . . .o
: These are derived from the power flow models.
The lower heating value (LHV) of a fuel relates to the energy and mass rates as 𝑑𝐸𝑖
𝑑𝑡 =(𝐿𝐻𝑉 )𝑖𝑑 𝑚𝑖
𝑑𝑡 .
•
Custom outputs: Outputs specific to the vehicle that can be used for power sizing analyses or simply for reporting.
Examples include shaft power requirements of individual propulsors, lift-to-drag ratios, propulsor efficiencies, etc.
B. Flight Mechanics Model (FMM)
Fig. 4 Flight Mechanics Model (FMM) showing setup for power,flightpath, and acceleration solution modes
The Flight Mechanics Model (FMM), shown in Fig. 4, includes the APPM as a component. Each flight condition is
treated within the FMM as a case of dynamic equilibrium in which some or all of the following residuals must be driven
to zero: (i) x-axis force residual, in wind axes, (ii) z-axis force residual, in wind axes, (iii) pitching moment residual, in
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body axes, (iv) rolling moment residual, in body axes, and (v) yawing moment residual, in body axes.
𝜆𝑥=1
𝑚𝐹𝑥𝐴−𝑔sin 𝛾−¤
𝑉→0axial force residual
𝜆𝑧=1
𝑚𝐹𝑧𝐴+𝑔cos 𝛾+𝑉¤𝛾→0normal force residual
𝜇𝑦=𝑀𝑦𝐴→0pitching moment residual
𝜇𝑥=𝑀𝑥𝐴→0rolling moment residual
𝜇𝑧=𝑀𝑧𝐴→0yawing moment residual (1)
𝐹𝑥𝐴, 𝐹𝑧𝐴,
and
𝑀𝑦𝐴, 𝑀𝑥𝐴, 𝑀𝑧𝐴
are outputs from the APPM. For nominal flight conditions, a 3
×
3 square system
(considering 𝜆𝑥, 𝜆𝑧, 𝜇𝑦residuals) is solved in one of the following modes, which are depicted graphically in Fig. 4:
1)
Power Mode: The flight condition (
𝑉, ℎ
), flightpath (
¤
ℎ
/
𝛾
,
¤𝛾)
, and acceleration (
¤
𝑉
) are specified. The required
throttle setting (𝛿𝑡), equilibrium AOA (𝛼), and trim control setting (𝛿𝑐) are calculated.
2)
Flightpath Mode: The flight condition (
𝑉, ℎ
), flightpath curvature (
¤𝛾
), acceleration (
¤
𝑉
), and throttle setting (
𝛿𝑡
)
are specified. The resulting flightpath (
¤
ℎ
/
𝛾
), equilibrium AOA (
𝛼
), and trim control setting (
𝛿𝑐
) are calculated.
3)
Acceleration Mode: The flight condition (
𝑉, ℎ
), flightpath (
¤
ℎ
/
𝛾
), and throttle setting (
𝛿𝑡
) are specified. The
resulting acceleration ( ¤
𝑉), equilibrium AOA (𝛼), and trim control setting (𝛿𝑐) are calculated.
The FMM is solved in the trim mode for off-nominal/post-failure flight conditions, where a 5
×
5 system is solved by
also considering the x-axis and z-axis moment residuals (respectively rolling and yawing moments), as well as two
additional control effectors along these two axes. This mode is used for power sizing analyses in non-nominal VFM
scenarios, such as propulsor failure. Trimming the aircraft in these scenarios may necessitate significantly more power,
which may influence the sizing of certain propulsion system components.
III. Configuration and Propulsion System Overview
Fig. 5 TW-02 Pangolin configuration overview
The general arrangement of the Tilt-Wing (TW) vehicle "TW-02 Pangolin", studied in this paper, is shown in Fig. 5.
The configuration features a tilting wing with six propulsors, three mounted on each wing. The propulsors are designed
to provide necessary thrust in forward flight mode as well as support the vehicle in vertical flight mode. The vehicle is
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Fig. 6 Power flow model
designed to take off vertically, powered by wing-mounted propulsors with wings tilted back in a vertical orientation.
There are two trim fans, each mounted at the nose and tail section of the fuselage, respectively. The trim fans are
designed to provide the necessary pitching moment to control the vehicle in the longitudinal axis in rotor-borne flight
mode. In VFM, roll control is achieved using differential pitch from the constant speed propulsors. The inboard and
outboard flaperons see airflow from the propulsor slipstream and are used to provide yaw control. As the vehicle
transitions from VFM to FFM, the wings are gradually tilted forward, and the propulsors are now used to provide
forward thrust as the vehicle gets wing-borne. The all-moving canards, which see relatively cleaner air, are used to
achieve longitudinal control when the vehicle is in transition mode, and the aft horizontal tail is rendered less effective
by the disturbed airflow from the fuselage and rotating wing. Once in forward flight mode, conventional control surfaces
are used to provide the necessary control. The flaperons on the wing and differentially moving canards are used for roll
control. The elevators (along with the canards) are used to provide control in the pitch axis. The rudders on the left and
right vertical stabilizers are used to achieve control in the yaw axis.
The vehicle features a turbo-electric (TE) propulsion system architecture with two turboshafts (TS-1 and TS-2)
powering all the propulsors and the trim fans as shown in Fig.6. There are two gearboxes (GB-1 and GB-2) connecting
each turboshaft to the four generators (GEN-1, GEN-2, GEN-3, and GEN-4), which provide power to all the motors (M-1,
M-2,..., M-NF, M-TF) through an electrical bus. In Fig. 6,
𝑃()
represents the component power outputs and
𝜂()
represents
the component efficiencies. The power requirements
𝑃𝑝,1, 𝑃 𝑝,2, ..., 𝑃 𝑝,6
of the six propulsors, and
𝑃𝑛 𝑓
and
𝑃𝑡 𝑓
required
by the nose and tail trim fans respectively are met by the motor power output
𝑃𝑚,1, 𝑃𝑚 ,2, ..., 𝑃𝑚,6, 𝑃𝑚 ,𝑛 𝑓 , 𝑃𝑚, 𝑡 𝑓
. In
case of a propulsor failure, there are two possible options:
(i)
To trim the vehicle using the remaining five propulsors, or
(ii)
To turn off the adjacent motor on the other half and operate using four propulsors. For this study, the latter is chosen
as an off-nominal case to size the propulsion system components. An emergency battery (BATT, EM) is installed to
provide surplus power
𝑃𝑏𝑎𝑡 𝑡 , 𝑒𝑚
needed when either of the turboshafts or gearboxes fails in vertical flight mode, and the
power demand is not met by the operating turboshaft. If such failure occurs in the cruise, the battery is not used, and the
vehicle is operated by the operating turboshaft engine.
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©«
ª®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®¬
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
11111111−𝜂𝑚0 0 0 0 0 0 0 0 0
00000000 −1 1 1 1 1 0 0 0 0 𝜏
00000000 0 1 1 0 0 −𝜂𝑔𝑒𝑛 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 1 0 −𝜂𝑔 𝑒𝑛 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 −𝜂𝑔 𝑏 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 −𝜂𝑔𝑏 0
00000000 𝜖1𝛼1𝛽1𝛾1𝛿10𝜁10 0 0
00000000 𝜖2𝛼2𝛽2𝛾2𝛿20 0 𝜁20 0
00000000 𝜖2𝛼3𝛽3𝛾3𝛿30 0 0 𝜁30
00000000 𝜖4𝛼4𝛽4𝛾4𝛿40 0 0 0 𝜏4
| {z }
𝐴𝑇𝐸

𝑃𝑚,1
𝑃𝑚,2
𝑃𝑚,3
𝑃𝑚,4
𝑃𝑚,5
𝑃𝑚,6
𝑃𝑚,𝑛 𝑓
𝑃𝑚,𝑡 𝑓
𝑃𝑏𝑢𝑠
𝑃𝑔𝑒𝑛, 1
𝑃𝑔𝑒𝑛, 2
𝑃𝑔𝑒𝑛, 3
𝑃𝑔𝑒𝑛, 4
𝑃𝑔𝑏, 1
𝑃𝑔𝑏, 2
𝑝𝑡𝑠 ,1
𝑃𝑡𝑠 ,2
𝑃𝑏𝑎𝑡 𝑡 , 𝑒𝑚

| {z }
𝑋𝑇𝐸
=

𝑃𝑝,1
𝑃𝑝,2
𝑃𝑝,3
𝑃𝑝,4
𝑃𝑝,5
𝑃𝑝,6
𝑃𝑛 𝑓
𝑃𝑡 𝑓
0
0
0
0
0
0
𝑏1
𝑏2
𝑏3
𝑏4

| {z }
𝐵𝑇𝐸
(2)
The power flow through each component in the TE architecture can be captured, as shown in Eq. 2, through a matrix
equation
𝐴𝑇 𝐸 𝑋𝑇 𝐸 =𝐵𝑇𝐸
. The first 14 equations of Eq. 2represent power balances across the components of Fig. 6
where
𝜏
acts as a switch for the emergency battery operation. The last four equations represent different closure relations
for component failure cases in the propulsion system. From a mathematical point of view, these closure relationships
make the system square and thus invertible. The closure relations are as follows:
1)
Nominal operation: Under nominal operations, it is assumed that the four generators share the total electrical
load equally (each contributing a quarter). This is enforced through the three closure relationships by setting
(i)
𝑃𝑔𝑒𝑛, 1=𝑃𝑏𝑢𝑠 /4⇐=𝛼1=1, 𝜖1=−1/4, 𝑏1=0
, (ii)
𝑃𝑔𝑒𝑛, 2=𝑃𝑏𝑢𝑠 /4⇐=𝛽2=1, 𝜖2=−1/4, 𝑏2=0
,
(iii)
𝑃𝑔𝑒𝑛, 3=𝑃𝑏𝑢𝑠 /4⇐=𝛾3=1, 𝜖3=−1/4, 𝑏3=0
, and (iv)
𝜏4=1, 𝑏4=0
, with all other closure variables
set to zero by default.
2)
Failure of one generator: The failure of one generator can be modeled by using the closure relationships to
enforce that the remaining three operational generators share the total electrical load. Since the generators are
identical, without loss of generality, the failure of Gen-4 can be modeled by setting (i)
𝑃𝑔𝑒𝑛, 1=𝑃𝑏𝑢𝑠 /4⇐=
𝛼1=1, 𝜖1=−1/4, 𝑏1=0
, (ii)
𝑃𝑔𝑒𝑛, 2=𝑃𝑏𝑢𝑠 /4⇐=𝛽2=1, 𝜖2=−1/4, 𝑏2=0
, (iii)
𝑃𝑔𝑒𝑛, 3=𝑃𝑏𝑢𝑠 /2⇐=
𝛾3=1, 𝜖3=−1/2, 𝑏3=0
, and (iv)
𝜏4=1, 𝑏4=0
with all other closure variables set to zero. The turboshaft
providing power to GEN-3 is penalized to provide more power.
3)
Failure of one turboshaft engine or gearbox with the emergency battery OFF (
𝜏=0
): In either scenario,
the shaft-power supplied to the two connected generators becomes zero, resulting in their power output also
becoming zero. Since both turboshaft engines are identical, without loss of generality, the failure of TS-1
or GB-1 can be modeled as (i)
𝑃𝑔𝑒𝑛, 1=0⇐=𝛼1=1, 𝑏1=0
, (ii)
𝑃𝑔𝑒𝑛, 2=0⇐=𝛽2=1, 𝑏2=0
,
(iii)
𝑃𝑔𝑒𝑛, 3=𝑃𝑏𝑢𝑠 /2⇐=𝛾3=1, 𝜖3=−1/2, 𝑏3=0
, and (iv)
𝜏4=1, 𝑏4=0
with all other closure variables set
to zero. This will enforce zero power output from the emergency battery.
4)
Failure of one turboshaft engine or gearbox with the emergency battery ON (
𝜏=1
): In case of high
power demands, especially in hover, the functional turboshaft is operated at maximum available power, and
the emergency battery is turned on to offset the power required by the motors. Since both turboshaft engines
are identical, without loss of generality, the failure of TS-1 or GB-1 can be modeled as (i)
𝑃𝑔𝑒𝑛, 1=0⇐=
𝛼1=1, 𝑏1=0
, (ii)
𝑃𝑔𝑒𝑛, 2=0⇐=𝛽2=1, 𝑏2=0
, (iii)
𝑃𝑡𝑠 ,2=𝑃𝑡 𝑠 , 𝑎𝑣 ⇐=𝜁3=1, 𝑏3=𝑃𝑡 𝑠, 𝑎𝑣
, and
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(iv) 𝑃𝑔𝑒𝑛, 3=𝑃𝑔𝑒𝑛,4⇐=𝜏4=0, 𝑏4=0, with all other closure variables set to zero.
The
𝐴𝑇 𝐸
matrix is fully known with the knowledge of component efficiencies and the system operating modes. The
𝐵𝑇 𝐸
matrix is defined based on the propulsor requirements obtained by solving the APPM and the operating mode.
Inverting the
𝐴𝑇 𝐸
matrix and multiplying it with
𝐵𝑇 𝐸
will give the power requirements of each propulsion system
component 𝑋𝑇𝐸 =𝐴−1
𝑇 𝐸 𝐵𝑇 𝐸 .
IV. Technical Analysis Approach
A. Aero-propulsive Model Development
The aero-propulsive model uses an embedded strip-theory based approach for lifting surfaces, blade element
momentum theory (BEMT)- based propeller performance model, and look-up tables for the remainder of the geometry.
1. Downwash Modeling of Lifting Surfaces
Lifting surfaces are divided into a number of finite strips as shown in 7. Each strip has a control point located at
the aerodynamic center of the longitudinal midsection of the strip. The method of reference [
52
] based on simplified
lifting-surface theory for lifting surfaces with symmetrical loading is used to compute spanwise loading ( dimensionless
circulation) distribution
𝐺
over the semi-span of lifting-surfaces. Charts that plot the span loading per unit flap,
𝐺/𝛿
,
Fig. 7 Strip theory representation of a lifting surface with a control surface
for full wing-chord (
𝑐𝑓/𝑐=1
), partial-span and full-span flaps for a range of wing geometry, airfoil, and operating
conditions parameter are converted into look-up tables and implemented as gridded interpolants. Since the full
wing-chord and full-span flaps are essentially wings. The angle of control surface deflection,
𝛿
, is replaced by the
geometric angle of attack
𝛼
measured relative to zero-lift-angle of attack,
𝛼𝐶𝐿=0
. When applied to the lifting surfaces,
𝐺/𝛿is called 𝐺/𝛼, and is queried at the aerodynamic center of the mid-section of each strip.
𝐺
𝛼
=𝑓𝛽𝐴
𝑘,Λ𝛽, 𝜆(3)
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where
𝜂
is the dimensionless lateral coordinate of the strip mid-section,
𝛽𝐴/𝑘
is the aspect ratio parameter that takes
into account the compressibility and section lift-curve slope through compressibility parameter
𝛽
and
𝑘
,
𝑘
is the ratio of
section lift curve slope at any span station to
2𝜋/𝛽
at the same Mach number,
Λ𝛽
is the sweep parameter including the
effect of compressibility and 𝜆is the wing taper ratio.
𝐺/𝛼
does not take into account the geometric twist of the wing. However, the effect of twist, if present, is captured
using strip-theory based approach when querying the section lift curve for lift coefficient. The loading coefficient of
the wing,
𝐺/𝛼
, is used to calculate loading
𝐺
, which is then used to calculate circulation distribution
Γ
. Using the
fundamental equation of Prandtl’s lifting line theory, induced angle of attack,
𝛼𝑖
is obtained for each strip with lateral
coordinate
𝑦𝑜
and seeing free-stream velocity of
𝑉∞
by summing the effect of circulation gradient due to all other strips
at lateral coordinate
𝑦
on the strip at
𝑦𝑜
. Once the induced angle of attack is computed, the effective angle of attack
is computed, which is used to query section aerodynamic characteristics of the lifting surface airfoil. The following
equations mathematically describe the process of computing the lift coefficient at each strip.
𝐺=𝐺
𝛼×𝛼(4)
Γ = 𝐺
𝑏𝑉∞
(5)
𝛼𝑖(𝑦0)=1
4𝜋∫𝑏/2
−𝑏/2
1
𝑉∞(𝑦0)
𝑑Γ/𝑑𝑦
𝑦0−𝑦𝑑𝑦 (6)
𝛼𝑒 𝑓 𝑓 =𝛼−𝛼𝑖(7)
𝑐𝑙=𝑓(𝛼𝑒 𝑓 𝑓 )(8)
The induced drag
𝑐𝑑𝑖
at each strip is also computed based on the downwash and circulation distribution. The strip
profile drag coefficient, 𝑐𝑑, and pitching moment coefficient, 𝑐𝑚are queried from section aerodynamic data.
The effect of wing downwash on the horizontal tail was modeled using the method of reference [
53
] as presented in
[
36
]. First of all, downwash gradient
(𝑑𝜖/𝑑𝛼)𝑣
was determined in the plane of symmetry at the height of the vortex
cores, and the longitudinal station of the quarter-chord point of the horizontal-tail mean aerodynamic chord. Then,
this value was corrected for the position of the horizontal tail above or below the trailing vortices and the span of the
horizontal tail to obtain the average downwash acting on the horizontal tail
𝑑𝜖/𝑑𝛼
. Finally, the average downwash acts
on the horizontal tail by integrating the average downwash gradient. The initial downwash angle
𝜖𝑜
was taken to be
zero for the zero-lift-angle of attack of the wing. A lookup table in the form of a gridded interpolant was implemented
in the sizing framework ( in the Aero Updater I block in Fig. 8) to query the downwash angle for any wing angle
of attack during mission analysis. The effect of canard downwash on the wing was crudely approximated using the
above-described method by assuming the canard downwash evenly influences the wing inboard of the canard tips as
suggested by Raymer(2012) [54].
The implementation of the aerodynamic model is done at two levels, as shown in Fig. 8based on the inputs to
the APPM. The first level, labeled as Aero Updater I, gives aerodynamic values such as span loading coefficient and
downwash interpolants based on the input parameters, such as aircraft geometry and typical operating Mach number,
that can change between the sizing iterations but remain constant within a sizing iteration. The second level, labeled as
Aero Updater II, gives strip-level force and moments based on the input parameters, such as angle of attack and control
surface deflection, which can change within a sizing iteration based on actual flight conditions.
One limitation of the current approach lies in that the effect of the fuselage on the wing lift distribution is not
accounted for. One potential solution is to use the conformal mapping technique [55]
2. Modeling of Control surfaces
Control surfaces deflections are modeled based on the change of span loading
𝐺
distribution when they deflect.
No distinction is made between control surfaces of different types, such as flap or aileron, in the conventional sense.
Span loading based on anti-symmetrical loading distribution from reference [
38
] is taken to model the control surfaces
independent of whether there lies a counterpart control surface about the aircraft plane of symmetry or not. Since
the anti-symmetrical loading drops to zero at the wing root, the distribution captures the decrease in loading near the
fuselage-wing or fuselage/ boom-tail junction for "flap" type control surfaces which are assumed to deflect symmetrically
about the plane of symmetry.
To model the control surfaces, first, the span-loading coefficient,
𝐺/𝛿
, for the full-wing chord control surface is
computed in a similar manner to
𝐺/𝛼
for the wing. In this case, the wing zero-lift angle of attack,
𝛼𝐶𝐿=0
, is replaced
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Fig. 8 Implementation of the aerodynamic model within PEACE framework (Fig. 2)
by the angle of control surface deflection
𝛿
. For a control surface that extends outboard from the plane of symmetry, the
loading is found by interpolating the data for inboard control surfaces extending from the plane of symmetry to the
outboard stations. For a control surface of arbitrary span, not starting at the plane of symmetry, loading distribution
is found by calculating the difference between the loading of two control surfaces which extend from the plane of
symmetry to the outboard end of the control surface and from the plane of symmetry to the inboard end of the control
surface respectively. This is possible because span loading is theoretically additive. Since control surfaces are treated
individually, the effect of differential control surface deflection is accounted for directly.
Once the
𝐺/𝛿
is computed based on the wing parameters and location of the control surface, the additional lift
coefficient due to the control surface is obtained using Eq. 9.
Δ𝑐𝑙=2𝑏
𝑐
𝐺
𝛿𝛼𝛿𝛿(9)
where
𝑏
is the span of the parent lifting surface,
𝑐
is the chord distribution over the span,
𝛼𝛿
is an empirical correction
factor called lift-effectiveness parameter obtained as function flap deflection and flap chord to airfoil chord ratio [
36
].
𝛼𝛿
parameter converts the spanwise loading distribution of full-wing chord control surfaces to the spanwise loading
distribution of partial wing-chord control surfaces. Because the spanwise loading is additive, and the lift coefficient is
directly related to the span loading (refer to 9), the incremental lift coefficient due to control surface deflection is added
to the lift distribution of the parent lifting surface to obtain total lift distribution over the lifting surface. However, the
induced drag depends on the induced angle of attack, which is a function of circulation gradient (refer to 7); the induced
drag due to the control surface is determined first by finding the total induced angle of attack by adding the spanwise
loading due to lifting surface and the control surface. The profile drag increment is computed in two steps [
36
]: (i)
airfoil section drag coefficient with deflected control surface is queried as a function of deflection and flap-to-airfoil
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chord ratio, and (ii) the value is corrected for the effect of wing taper ratio and control surface span ratio by an empirical
factor.
Γ𝑡𝑜𝑡 = Γ𝐿 𝑆 +Γ𝐶𝑠 (10)
The spanwise loading due to the control surface is added or subtracted based on whether the deflection is down or up
respectively. One limitation of the present analysis lies in the treatment of the cambered control surfaces as if they were
symmetric. One potential solution could be to measure the deflection relative to the zero-lift-line, which will be looked
at in the future.
3. Modelling of Non-Lifting Surfaces
The aerodynamic force and moment contributions of non-strip components such as fuselage, nacelles, and landing
gear were captured in the form of lookup tables and implemented as gridded interpolants as a function of the angle of
attack and sideslip angle. To create the lookup table, the complete baseline geometry was evaluated over a range of
angles of attack and sideslip angle using FlightStream®[56].
B. Propulsor Model
QMIL [
39
] and QPROP [
40
] tools were used to determine the blade design for the six propulsors and the trim
fans. QMIL designs a propeller based on the minimum induced loss (MIL) condition. It requires blade airfoil sectional
properties (which were obtained using XFOIL [
57
]), the number of blades, the propeller diameter, design lift coefficient,
altitude, revolution per minute (RPM), and either thrust required or power supplied. With this information, QMIL
determines the blade chord and twist distribution along the span of the propeller blade to yield the MIL condition.
QPROP can be used to run a propeller designed using QMIL over a range of off-design conditions with different
combinations of freestream velocity, RPM, and blade pitch setting.
For trim fans, the design requirements were set up so that each fan contributes 5% of the total hover thrust requirement.
The airfoil chosen for the trim fans was a symmetric NACA0006 airfoil because the design goal was to generate a
pitching moment and not contribute to the total lift requirements in VFM. The chord and blade pitch distribution as a
function of normalized radius were generated and the trim fans were evaluated using embedded BEMT coupled to a
seven-state Pitt-Peters inflow model with wake distortion effects [
58
], whose steady-state solutions were computed to
give the isolated loads for both axial and edgewise flow conditions.
QMIL/QPROP setup was integrated into PEACE to design the six propulsors, where a new blade design was created
as the vehicle size gets updated after each sizing iteration. The propulsor blades were designed to be efficient in cruise
for the given MTOM and design cruise speed. The propulsors so designed were then evaluated at hover flight conditions
to ensure that the thrust requirements were met. As the vehicle geometry gets updated, QMIL is invoked inside the
vehicle system updater to create a new blade design for the propulsors based on the updated MTOM and disk loading.
In APPM, the propulsor loads were evaluated using BEMT coupled with the seven-state Pitt-Peters inflow model.
C. Propeller Slipstream Modeling
The effect of the propeller slipstream on the wing lying immediately downstream is modeled, which renders the
control surfaces (flaperons) active in VFM. The propeller axis is assumed to be aligned with the chord line of the wing
with no angular or normal offsets. The relevant geometric parameters are propeller radius
(𝑅)
, diameter
(𝐷)
, disc area
(𝐴=𝜋𝑅2=𝜋𝐷2/4)
, wing chord at propeller location
(𝑐)
, and distance from propeller disc to wing mid-chord
(𝑠)
. The
induced axial velocity
𝑣𝑖
at each propeller disc is calculated as modeled by Cook and Hauser [
59
] using momentum
theory,
𝑣𝑖=1
2 −𝑣𝑛+𝑣2
𝑛+2𝑇
𝜌 𝐴 !,(11)
where
𝑣𝑛
is the component of freestream velocity normal to the disc, and
𝑇
is the propeller thrust. To avoid having
to assume (as in [
59
]) that the slipstream is fully contracted by the time it reaches the wing and that the contracted
streamtube diameter is invariant to freestream velocity changes, the slipstream development was based on the work of
Stone [60], who used a formula developed by McCormick [61],
𝑘𝑑=1+𝑠
√𝑠2+𝑅2(12)
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where
𝑘𝑑
is the slipstream development factor. As
𝑠→ ∞
,
𝑘𝑑→2
(for a fully developed slipstream). The axial induced
velocity downstream of the disc is related to that at the disc by
𝑣′
𝑖=𝑘𝑑𝑣𝑖
[
60
]. A further multiplicative factor
𝛽≤1
is
introduced, such that
𝑣′
𝑖=𝛽𝑘 𝑑𝑣𝑖
, to account for a finite slipstream height. Based on the effective
𝛽
values computed by
Patterson [62] from the results presented by Ting et al. [63], 𝛽is expressed as follows:
𝛽=−0.3612 𝑅
𝑐5
+2.2635 𝑅
𝑐4
−5.0715 𝑅
𝑐3
+4.3912 𝑅
𝑐2
−0.3255 𝑅
𝑐,0≤𝑅
𝑐<1.9
𝛽=1,𝑅
𝑐≥1.9(13)
The current work assumes that the induced velocities
𝑣𝑖, 𝑣′
𝑖
are uniform over the disc. For strips that are influenced by
the slipstream, the direct flow velocity 𝑉𝑠and direct AOA 𝛼𝑑𝑖𝑟 computed previously are modified as follows:
𝑉′
𝑠=(𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝑣′
𝑖)2+ (𝑉𝑠sin 𝛼𝑑𝑖𝑟 )2
𝛼′
𝑑𝑖𝑟 =tan−1𝑉𝑠sin 𝛼𝑑𝑖𝑟
𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝑣′
𝑖(14)
It is seen from Eq. 14 that the effect of the propeller slipstream (
𝑣′
𝑖
) is to increase the velocity over affected strips and
reduce the magnitude of the flow incidence angle. To compute the contracted streamtube diameter
𝐷′
, the continuity
equation is applied to equate the mass flow rates at the propeller disk (disc area
𝐴
, axial flow velocity
𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝑣𝑖
)
and the midchord location on the wing (streamtube area 𝐴′, axial flow velocity 𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝑣′
𝑖):
(𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝑣𝑖)𝐴=(𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝑣′
𝑖)𝐴′=⇒𝐴′=𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝑣𝑖
𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝛽𝑘𝑑𝑣𝑖
𝐴=⇒𝐷′=𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝑣𝑖
𝑉𝑠cos 𝛼𝑑𝑖𝑟 +𝛽𝑘𝑑𝑣𝑖
𝐷(15)
Since
𝑘𝑑≥1
, it follows that
𝐷′≤𝐷
. Knowing the spanwise location of the propeller and the streamtube diameter
𝐷′
at a given operating condition, the strips that are fully immersed in the propeller slipstream can be readily determined.
For a strip that falls partially within the streamtube, the average of the freestream and streamtube velocities is used.
D. Battery Modeling
Battery mass can be estimated based on both energy requirement
𝐸𝑟𝑒𝑞
(computed by the Mission Analyzer) and
peak power requirement
𝑃𝑝𝑒𝑎 𝑘
(computed by the Power Sizer). The battery C-rate,
𝐶
, the inverse of the time (in hours)
needed to fully discharge the battery at a steady discharge rate, relates the battery-specific power
(𝑃/𝑀)𝑏𝑎𝑡 𝑡
and specific
energy (𝐸/𝑀)𝑏𝑎𝑡 𝑡 as (𝑃/𝑀)𝑏 𝑎𝑡 𝑡 =(𝐸/𝑀)𝑏𝑎𝑡𝑡 ×𝐶. The battery mass is estimated as
𝑚𝑏𝑎𝑡 𝑡 =max 𝐸𝑟 𝑒𝑞
(𝐸/𝑀)𝑏𝑎𝑡 𝑡
,𝑃𝑝𝑒𝑎 𝑘
(𝑃/𝑀)𝑏𝑎𝑡 𝑡 (16)
During the evaluation of the power sizer, an emergency battery was used just for the off-nominal cases with one
turboshaft and/or one gearbox failure, where the power requirements were not met by the operating turboshaft and/or
gearbox. The emergency battery was required to provide the necessary peak power for two minutes (C-rate set to
30) [
64
], and thus the mass of the battery was determined using the peak power requirement and specific power of the
battery.
E. Turboshaft Modeling
The power lapse, weight, specific fuel consumption, length, and diameter of turboshaft engines were estimated based
on the curve fits that were developed in prior work [
44
]. A two-dimensional lookup table expressing the ratio of available
power to rated power at sea-level (SL) static conditions as a function of airspeed and altitude was generated to create the
power-lapse model, based on data presented in [
13
]. The relationships for weight
𝑊𝑡𝑠
, specific fuel consumption
𝑠 𝑓 𝑐
,
length ℓ𝑡𝑠 , and diameter 𝑑𝑡 𝑠 were obtained as functions of rated sea-level horsepower (𝑠ℎ 𝑝)as follows:
𝑊𝑡𝑠 [lb] =−0.0001 (𝑠ℎ 𝑝)2+0.5547(𝑠 ℎ 𝑝) − 20.519
𝑠 𝑓 𝑐 [lb/hp-h] =1.8784 (𝑠ℎ𝑝)−0.173
ℓ𝑡𝑠 [in] =3.857(𝑠ℎ𝑝)0.373
𝑑𝑡𝑠 [in] =10.112(𝑠 ℎ 𝑝)0.12
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The relationship used to estimate
𝑠 𝑓 𝑐
captures its decreasing trend with rated horsepower but does not capture the effect
of flight condition or the deterioration of
𝑠 𝑓 𝑐
at part power operation. Though this is a current limitation, the turboshaft
operating points considered in this work involve operation at relatively high power settings.
F. Structural and Systems Mass Properties Estimation
Weight estimation relationships used to evaluate the mass properties of the vehicle were based on general aviation
(GA) aircraft from [
12
–
14
], which were developed based on regression analysis applied to weight data of existing
aircraft. The relationships used in this study are summarized in [
44
]. For components for which multiple weight
equations were available from different sources, the average of the computed weights was used. Component CGs
were computed based on their geometry, and their effects on the aircraft CG was determined based on the mass
and location of each component. Moments and products of inertia of each component were computed about the
respective component centroidal axes. Parallel axis theorem in three-dimensional form was used to transfer them to
the body-fixed frame of reference. Smaller components were approximated as a point mass, with inertia contributions
𝐼𝑥𝑥 =𝑚(𝑦2+𝑧2), 𝐼𝑦 𝑦 =𝑚(𝑥2+𝑧2), 𝐼𝑧 𝑧 =𝑚(𝑥2+𝑦2)
, where
𝑚
is the component mass and
(𝑥, 𝑦, 𝑧)
its position expressed
in the aircraft body axes.
G. Trim Setup and Control Allocation
Table 1 List of control effectors
# Symbol Description Unit
1𝛿𝑐1Left cananrd deg
2𝛿𝑐2Right canard deg
3𝛿𝑓1Flaperon, left wing, outboard deg
4𝛿𝑓2Flaperon, left wing, inboard deg
5𝛿𝑓3Flaperon, right wing, inboard deg
6𝛿𝑓4Flaperon, right wing, outboard deg
7𝛿𝑒1Left elevator deg
8𝛿𝑒2Right elevator deg
9𝛿𝑟1Left rudder deg
10 𝛿𝑟2Right rudder deg
11 𝛿𝑤Wing angle deg
12-17 𝛽1−𝛽6Propulsor pitch deg
18-19 𝛽𝑛 𝑓 , 𝛽𝑡 𝑓 Trim fan pitch deg
20-25 𝑁1−𝑁6Propulsor RPM RPM
26-27 𝑁𝑛 𝑓 , 𝑁𝑡 𝑓 Trim Fan RPM RPM
The general trim problem setup for the TW-02 configuration involves the state variables (angle of attack
𝛼
, sideslip
angle
𝛽
, bank angle
𝜙
, turn rate
¤
𝜓
, and heading
𝜓
) and control variables (lateral control
𝑢𝑙𝑎𝑡
, longitudinal control
𝑢𝑙𝑜𝑛
,
directional control
𝑢𝑑𝑖𝑟
, propulsor collective pitch
𝛽0
, and wing angles
𝛿𝑤
), which allow trim solutions to be found
for climbing/descending, turning, and asymmetric flight conditions in addition to steady, level, unaccelerated flight
(SLUF). For SLUF, the bank angle
𝜙
, turn rate
¤
𝜓
, and flightpath angle
𝛾
are constrained to zero. The normalized control
variables
𝑢𝑙𝑎 𝑡 , 𝑢𝑙𝑜𝑛 , 𝑢𝑑𝑖𝑟 ∈ [−1,+1]
represent control effort about the lateral (roll), longitudinal (pitch), and directional
(yaw) axes. These variables map to control surface deflections and blade pitch angles per a control allocation logic. The
full list of control effectors is shown in Table 1. The generalized setup of the trim problem as described above allows
trim solutions to be sought not only for SLUF, but also for turning flight, climbing/descending flight, and asymmetric
(sideslipping) flight conditions. For the sizing studies, the trim problem is solved for only the cases which involve
symmetric flight conditions.
The goal of the control allocation logic is to map the propeller pitch settings and control surface deflections
to three normalized control variables: (i)
𝑢𝑙𝑎𝑡 ∈ [−1,+1]
for roll axis, (ii)
𝑢𝑙𝑜𝑛 ∈ [−1,+1]
for pitch axis, and (iii)
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𝑢𝑑𝑖𝑟 ∈ [−1,+1]for yaw axis. The blade pitch settings of the propulsors and the trim fans are computed as follows:

𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽𝑛 𝑓
𝛽𝑡 𝑓

=

1.0+1.0 0.0
1.0+1.0 0.0
1.0+1.0 0.0
1.0−1.0 0.0
1.0−1.0 0.0
1.0−1.0 0.0
0.0 0.0+1.0
0.0 0.0−1.0


𝛽0
𝛽𝜙
𝛽𝜃
, 𝛽𝜙=𝛽𝑚𝑎 𝑥
𝜙𝑢𝑙𝑎𝑡 𝐾𝛽𝜙, 𝛽𝜃=𝛽𝑚𝑎 𝑥
𝜃𝑢𝑙𝑜𝑛𝑔 𝐾𝛽𝜃(17)
In Eq. 17,
𝛽0
applies to all rotors and is used to create net changes in thrust, and the blade pitch increments
𝛽𝜙
and
𝛽𝜃
are used to affect roll and pitch control respectively as outlined previously.
The control surface mappings are defined by the normalized input multiplied by the maximum commanded deflection
angle. The control surface deflections are evaluated as
𝛿𝑐1, 𝛿𝑐2=+𝐾𝑒𝜃𝛿𝑐±𝐾𝑒𝜓𝛿𝑟, 𝛿𝑐=𝑢𝑙 𝑜𝑛 𝛿𝑚𝑎𝑥
𝑐, 𝛿𝑟=𝑢𝑑𝑖𝑟 𝛿𝑚 𝑎𝑥
𝑟
𝛿𝑓1, 𝛿 𝑓2=±𝐾𝑒𝜙𝛿𝑓∓𝐾𝑒𝜓𝛿𝑟, 𝛿 𝑓=𝑢𝑙𝑎 𝑡 𝛿𝑚𝑎𝑥
𝑓, 𝛿𝑟=𝑢𝑑𝑖𝑟 𝛿𝑚 𝑎𝑥
𝑟
𝛿𝑓3, 𝛿 𝑓4=∓𝐾𝑒𝜙𝛿𝑓±𝐾𝑒𝜓𝛿𝑟, 𝛿 𝑓=𝑢𝑙𝑎 𝑡 𝛿𝑚𝑎𝑥
𝑓, 𝛿𝑟=𝑢𝑑𝑖𝑟 𝛿𝑚 𝑎𝑥
𝑟
𝛿𝑒1, 𝛿𝑒2=−𝛿𝑒, 𝛿𝑒=𝑢𝑙 𝑜𝑛 𝛿𝑚𝑎 𝑥
𝑒
𝛿𝑟1, 𝛿𝑟2=+𝛿𝑟, 𝛿𝑟=𝑢𝑑𝑖 𝑟 𝛿𝑚𝑎𝑥
𝑟
(18)
Parameters
𝐾𝛽𝜙, 𝐾𝛽𝜃, 𝐾𝑒𝜙, 𝐾𝑒𝜓
are wash-in or wash-out functions that determine the extent to which a control
effector is used for roll, pitch, or yaw control as a function of wing angle. Fig 9shows an example case where the wing
angle increases as the vehicle transitions from FFM to VFM. The wash-out functions for the blade pitch variables are
linear (as shown in Table 2), washing in or out the desired effector as the wing angle decreases for attitude control.
Scheduling these parameters with respect to wing angle is synonymous with scheduling with respect to airspeed in
this sense. The ranges for control effectiveness parameter wash-in/wash-out were determined through analysis of trim
condition control inputs.
Table 2 Wash-in wash-out schedules (linear variations between data points)
𝛿𝑤90+ 80 70 60 50 40 30 20 10-
𝐾𝛽𝜙1 1111110 0
𝐾𝛽𝜃1 1111111 1
𝐾𝑒𝜙0 0000000 1
𝐾𝑒𝜓1 1110000 0
H. Resizing Rules
The geometry update rules are functions that relate component dimensions and positions to top-level aircraft
parameters such as MTOM, wing loading (WL), and disc loading (DL). The geometry is updated after each sizing
iteration to satisfy the preset update rules. The major rules defined for sizing this vehicle are as follows:
1)
The main wing is resized to maintain a wing loading of 195 kg/m
2
(40 lb/ft
2
), based on the main wing planform
area and referred to MTOM. An aspect ratio of 10, a taper ratio of 0.5, and an unswept trailing edge are
maintained. During trade studies, these parameters are changed in the geometry update rules from the baseline
setup, and the effects on the overall vehicle size are studied.
2)
The canard is resized to maintain a canard volume ratio
∗
of 0.15, an aspect ratio of 9, a taper ratio of 0.5, and an
unswept trailing edge. The horizontal stabilizer is resized to maintain a volume ratio of 1.00, aspect ratio of 6,
∗
Volume ratio is defined as NUM/DEN, where NUM = [planform area]
×
[moment arm] and DEN = [reference area]
×
[reference length]. The
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Fig. 9 Transition from wing-borne to rotor-borne flight
taper ratio of 0.8, and an unswept trailing edge. The vertical stabilizers are resized to maintain a volume ratio of
0.05, an aspect ratio of 3, and an unswept trailing edge. The horizontal stabilizer tip chord is calculated based on
the chord of the vertical stabilizer (to allow for mounting, as shown in Fig. 5).
3)
The propulsor diameter is determined so as to maintain a disk loading of 73 kg/m
2
(15 lb/ft
2
), referred to hover
conditions at MTOM and based on the combined disk area of all six propellers. But there is no guarantee that this
can be maintained when the WL is high, and DL is low, causing conflict between propulsor arcs. During such
cases of conflict, the disk loading is a fall-out parameter and is computed from the largest available propulsor
diameter and the current MTOM. Propulsor Nacelles and motors share the same spanwise coordinates as the
respective propellers.
4)
The fuselage comprises the following four sections: nose-cone, front cabin, aft cabin, and tail-cone. The
dimensions of the fuselage are not sized in this work. The mounting stations of the canards, wings, and horizontal
stabilizers are specified in terms of normalized fuselage length. Canards are mounted in front of the front firewall,
and the wings are located so that the reference point is at the target CG to facilitate the wing-tilt without changing
the CG location, and the horizontal stabilizers are stationed at the normalized fuselage station of 0.98 from the
nose.
The effects of the changes in the geometric parameters like wing loading, wing aspect ratio, and wing taper ratio
were also studied by modifying the geometry update rules accordingly.
V. Results
The parametric aero-propulsive model was integrated into PEACE, and a tilt-wing type advanced air mobility
vehicle was sized for a given design mission. Integration of the semi-empirical model facilitated the rapid evaluation
of aerodynamic characteristics based on the vehicle geometry alone. This allowed the trade studies by varying wing
geometry parameters from a baseline model, and evaluate the vehicle weight for different cases with minimal wait time.
The discussion follows a comparison study of the parametric aerodynamic model with a higher fidelity program, sizing
of propulsion system components for different nominal and off-nominal flight conditions (power sizing), and overall
vehicle sizing and analysis using the parametric aero-propulsive model. Results from the trade studies performed by
varying the geometry parameters are discussed towards the end of the section.
A. Aerodynamics
To study how well the embedded model described in section IV agrees with a truth model, different aero-
dynamic characteristics were obtained by varying the lifting surface geometry and compared with results from
FlightStream®reduced-order model for the same geometries. Circulation distributions over straight tapered wings of
aspect ratio 8 and 10, a taper ratio of 0.5 and 0.8, and constant wing loading are shown in Fig. 10 for semispan of the
wing. Wing with an aspect ratio of 8 and taper ratio of 0.5 is presented as a baseline for comparison. In the first subplot,
planform area is that of the surface in question. The moment arm is measured from its aerodynamic center to that of the wing. The reference area is
the wing planform area. For horizontal stabilizers and canards, the reference length is the wing mean aerodynamic chord. For vertical stabilizers, it is
a wingspan.
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as the taper ratio of the wing with an aspect ratio of 8 increases from 0.5 to 0.8, the magnitude of circulation distribution
decreases in the inboard region and increases in the outboard region, as expected, to conform with the resulting planform
distribution of the wing. In the second subplot, as the aspect ratio increases from 8 to 10, the magnitude of circulation
distribution over the wing decreases, as the lift per unit span required to maintain the same wing loading decreases. In
both cases, the embedded model agrees well with the FlightStream reduced-order model.
Fig. 10 Circulation (Γ) distribution for straight tapered wings
The wing level aerodynamic coefficients were obtained for individual lifting surface components: canard, wing,
horizontal tail, and vertical tail of the aircraft geometry using the embedded model and FlightStream®. In doing
so, the effect of the downwash of the forward lifting surface on the after lifting surface was not implemented since
the comparison was made with FlightStream®reduced-order model of the same nature. Using FlightStream®, two
categories of results were obtained. In the first category, aerodynamic coefficients were obtained for individual
components. In the second category, aerodynamic coefficients were obtained for components in the presence of other
components. For example, first, the analysis was done for the left wing only, and the analysis was done for the left wing
in the presence of the fuselage, and then in the presence of the fuselage and tail. Since the implemented aerodynamic
model did not consider the effect of the fuselage on lifting surface lift distribution, it was desired to see if the presence
of the fuselage significantly alters the 3-D aerodynamic coefficients. The plot of aerodynamic coefficients of the whole
aircraft, with all lifting and non-lifting components, is shown in Fig. 11. The component-wise plot of the end result of
the second category, a lifting surface in the presence of all other bodies, is shown in Figures A1 to A4 in Appendix A.
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The lift curve slopes
𝐶𝐿 𝛼
for all curves are published in the brackets. In computing the aerodynamic coefficients, the
exposed area of the whole wing is taken as the reference area, and the mean aerodynamic chord of the wing as the
reference length.
In all cases studied, the variation of lift coefficient with angle of attack,
𝐶𝐿vs.𝛼
from embedded model and
FlightStream®matches well. The variation of drag coefficient with angle of attack shows a good agreement in the
case of canard and little discrepancy for wing and horizontal stabilizer. The agreement for canard might be because
of the clean airflow and less interference due to the smaller height of the fuselage at the junction. The discrepancy
between wing and tail might be due to the difference in induced drag distribution. The induced drag, compared to lift, is
more sensitive to circulation distribution because induced drag, in addition to circulation distribution, is dependent on
the circulation gradient. Since the presence of a fuselage alters the circulation distribution and hence the circulation
gradient ( refer to Fig. A5 in Appendix A), the induced drag computed from the two methods did not exactly match.
The discrepancy in drag also resulted in the disagreement in the lift-to-drag ratio polar. The moment coefficient also
showed variation because of the difference in lift and drag coefficients. From Fig.11, it can be seen that the effect of
non-lifting surfaces at a higher angle of attack is destabilizing.
In the case of lift coefficient
𝐶𝐿
vs. angle of attack (
𝛼
) plot for the wing, a dotted line with slope based on
semi-empirical relation [
12
] is also shown. The wing aspect ratio is calculated based on the tip-to-tip span and total
area, including the fuselage portion of the lifting surfaces. The reference area is taken to be the exposed wing area.
Despite the small discrepancy, the aerodynamic results show reasonable agreement, in terms of values and trend, over a
normal range of angle of attack, and thus the embedded model is deemed suitable for the purpose of sizing.
Fig. 11 Variation of aerodynamic coefficients with angle of attack
𝛼
for whole aircraft based on wing exposed
area
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B. Power Sizing
The power sizing module evaluates the power flow relationships (Eq. 2) at specified nominal and off-nominal scenarios
to determine the constraining flight conditions that size propulsion system architecture components. The flight conditions
that were considered are summarized in Table 3. The cruise speed
𝑉𝐶
considered for power sizing was varied from
260-350 KTAS. The threshold speed
𝑉𝑡ℎ
between VFM and FFM was defined as
𝑉𝑡ℎ =(2/𝜌𝑆 𝐿 )(𝑊𝑡 𝑜 /𝑆𝑤)(1/𝐶𝐿𝑟𝑒 𝑓 )
,
where
𝜌𝑆𝐿
is sea-level density,
𝑊𝑡𝑜 /𝑆𝑤
the wing loading referred to MTOM, and with
𝐶𝐿𝑟𝑒 𝑓 =0.8
. FFM cases were
defined for nominal climb and cruise at sea-level, low altitude, and high altitude. Additionally, off-nominal cases for
turboshaft failure, generator failure, and the outermost propulsor failure were also evaluated. VFM cases were evaluated
at both sea-level and high, hot conditions. In addition to the nominal hover and vertical climb, off-nominal cases similar
to the FFM were considered. The high density altitude VFM cases were evaluated for 80% load capacity.
Table 3 Point performance constraints for power sizing (SL: sea-level; HH: high, hot; INOP: inoperative;
HOGE: hover out of ground effect, 𝑉𝑐: design cruise speed), 𝑉𝑡ℎ : VFM-FFM threshold speed)
Case Case Flight Airspeed Press. Density ΔISA R/C Payload
# Description Mode (knots) Alt (ft) Alt (ft) (◦C) (fpm) %
1 Cruise, high FFM 𝑉𝑐KTAS 10,000 10,000 - - 100
2 Cruise, low FFM 𝑉𝑐KTAS 3,000 3,000 - - 100
3 Cruise, degraded FFM 0.75 𝑉𝑐KTAS 3,000 3,000 - - 100
4 Climb, SL FFM 𝑉𝑡ℎ +10 KEAS 0 0 - 1,200 100
5 Climb, HH FFM 𝑉𝑡ℎ +10 KEAS 6,000 7,160 +10 1,000 100
6 Climb, HH, degraded FFM 𝑉𝑡 ℎ +10 KEAS 6,000 7,160 +10 500 100
7 HOGE, SL, VFM - 0 0 - - 100
8 Vert. climb, SL VFM - 0 0 - 1,000 100
9 HOGE, SL, GEN-1 INOP VFM - 0 0 - - 100
10 HOGE, SL, P-1,P-6 INOP VFM - 0 0 - - 100
11 HOGE, SL, TS-1 INOP VFM - 0 0 - - 100
12 HOGE, HH, VFM - 6,000 7,160 +10 - 80
13 Vert. climb, HH VFM - 6,000 7,160 +10 1,000 80
14 HOGE, HH, GEN-1 INOP VFM - 6,000 7,160 +10 - 80
15 HOGE, HH, P-1,P-6 INOP VFM - 6,000 7,160 +10 - 80
16 HOGE, HH, TS-1 INOP VFM - 6,000 7,160 +10 - 80
For each power sizing case, APPM yields the shaft-power requirements of the propulsors and the trim fans. The
power flow relations then relate these shaftpower requirements to the required power output of the associated propulsion
system component. The maximum power output of each component across all the power sizing cases was then used to
determine the rated power output of a component. All the nominal and off-nominal cases excluding the turboshaft failure
were evaluated, and the power rating of the turboshaft was determined based on the high-hot propulsor failure case in
hover (case 10: HOGE, SL, P-1,P-6 INOP). The generator was sized based on a generator failure case in a high-hot
hover scenario (case 14: HOGE, HH, GEN-1 INOP). The sized turboshaft was then used to evaluate the cases with one
turboshaft failure. Among all the off-nominal cases where a turbo-shaft failed, there were two specific scenarios (case
11: HOGE, SL, TS-1 INOP and case 16: HOGE, HH, TS-1 INOP) where the emergency battery was needed because
the available power from the operating turboshaft was not enough to satisfy the power requirements. The battery was
sized based on the peak power requirements using the most constraining case between the two (case 16).
C. Vehicle Sizing and Analysis
The aircraft is sized based on the inter-city travel mission profile as shown in Fig. 12. The sizing mission is
representative of a fixed-wing aircraft in terms of forward flight performance, as well as a rotary-wing aircraft in terms
of the ability to take off and land vertically. The mission includes vertical take-off and climb to 100 ft, followed by a
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Fig. 12 Design Mission Profile used to size TW-02 Pangolin
transition to FFM at a constant altitude. It is then followed by a climb in FFM to the altitude of 10000 ft and cruise
at 350 KTAS for the design mission range of 400 km (216 NM). At the end of the cruise, the vehicle descends to an
altitude of 2000 ft and loiters for 15 minutes, which is then followed by a descent to 100 ft and a transition to VFM at a
constant altitude before landing vertically. The distance covered during the transitions between VFM and FFM is not
included in the design range. The mission is performed with a maximum payload, which is fixed at 500 kg (1100 lb),
corresponding to the weight of five occupants and their baggage. The single trip distances and cruise speeds are varied
from the baseline, and the same design mission is flown to study their effects on the overall vehicle size.
For the baseline design mission, with the range of 400 km and cruise speed set at 350 KTAS at 10000 ft, the vehicle
was sized for maximum payload capacity, and the componentwise weight breakdown is summarized in Fig. 13. The
total maximum take-off mass (MTOM) of the vehicle was 4407 kg, with the structures and systems making up about
Fig. 13 Weight breakdown of a baseline TW-02 Pangolin sized for 400 km range mission
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41% and the propulsion components adding up to 38% of total gross weight. A more detailed weight breakdown for the
vehicle sized to the design mission can be found in Table B1 in Appendix B. The vehicle was sized for ranges 300 km
and 500 km as well, and the respective changes in the component weights can be observed from Table B1. In the results
that follow, the effects of changes in the geometry parameters, such as wing loading, wing aspect ratio, and wing taper
ratio, are also explored.
Fig. 14 Sweep results showing vehicle MTOM at different cruise speeds by varying wing aspect ratio (AR) and
wing taper ratio (TR) for wing loading (WL) of 40 𝑙𝑏/𝑓 𝑡2and 50 𝑙𝑏/𝑓 𝑡 2
The wing geometry parameters were changed from the baseline geometry, and the vehicle was sized for all the
combinations at three cruise speeds (
𝑉𝑐𝑟𝑢𝑖𝑠𝑒
= 300 KTAS, 350 KTAS, and 400 KTAS) for the same baseline range of
400 km and a maximum payload of 500 kg as shown in Fig. 14. Wing aspect ratio (AR) values of 8, 10, and 12, and the
wing taper ratio (TR) values of 0.4, 0.5, and 0.6 were used to evaluate the vehicle size keeping everything else constant.
It can be observed that the change in WL dominates overall vehicle size when compared to other parameters because of
the increased weight and drag of the larger wing. On the other hand, change in TR seems to have the least effect on the
Fig. 15 Vehicle sized for different range requirements and cruise velocities by selecting the optimal wing
geometry (AR = 10, TR = 0.4, WL = 50 𝑙𝑏/𝑓 𝑡2).
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overall vehicle size. The trend in overall MTOM increment with the increasing cruise flight speed can be observed
because of the increase in the energy requirements during the cruise. The increasing trend in vehicle MTOM with a
slight dip at AR of 10 was observed for most of the cases. The vehicle with the highest MTOM of 6127 kg was found to
have AR of 10, TR of 0.6, and WL of 40
𝑙𝑏/𝑓 𝑡 2
flown at 400 KTAS cruise speed, while the combination of AR, TR,
and WL of 10, 0.4, and 50
𝑙𝑏/𝑓 𝑡 2
respectively yielded the least MTOM of 3682 kg for the vehicle flown at the baseline
cruise speed of 350 KTAS.
The trade study performed by varying wing geometry parameters facilitated the selection of an optimal vehicle
design for the given design mission. Once the geometry for the lightest vehicle was determined, it was sized using the
fixed geometry for ranges varying from 300 km to 600 km, and the cruise speeds of 300 KTAS, 350 KTAS, and 400
KTAS, respectively, as shown in Fig. 15. A linear trend in vehicle MTOM was observed with the increasing range
requirements. The lower cruise speed requirements yielded lighter vehicles, while the increment in the cruise speed
increased the vehicle MTOM significantly. For example, the MTOM was seen to increase from 3692 kg to 4092 kg
(11% increase) when cruise speed increased from 300 KTAS to 350 KTAS, but a further increment in cruise speed to
400 KTAS resulted in the vehicle MTOM of 4872 kg (19% increase) for a given trip distance of 500 km. As expected,
with all else remaining the same, the increase in MTOM with increasing speed is due to the higher propulsive power and
energy requirements, and the resulting snowballing effects these have on aircraft sizing.
VI. Conclusion
This paper demonstrated the applicability of a rapid-evaluation aerodynamic model for sizing of an advanced air
mobility aircraft (i) by validating the aerodynamic model with the results of a commercial high-fidelity tool and (ii) by
performing sizing on a novel advanced air mobility concept vehicle. The aerodynamic model used strip-theory based
approach for the lifting surfaces and control surfaces. For lifting surfaces, a lookup table of spanwise loading coefficient
(dimensionless circulation) per unit angle of attack for wings with symmetrical loading distribution based on simplified
lifting surface theory was created and implemented as gridded interpolants. The lookup tables were queried for spanwise
loading coefficient for a range of aspect ratios, taper ratios, and sweep angle of the lifting surface. In the case of control
surfaces, a lookup table of spanwise loading coefficient per unit deflection for control surfaces with anti-symmetric
loading was created to generalize the method for all types of control surfaces. The lookup tables were queried for the
spanwise loading coefficient for the different spanwise locations of the full wing-chord control surfaces for the range of
parent lifting surface aspect ratio, taper ratio, and sweep angle. The empirical lift effectiveness parameter was then used
to convert the spanwise loading distribution of the full wing-chord control surface to the spanwise loading distribution
of the partial wing-chord control surface. The effects of the downwash of one lifting surface on the other lifting surface
were modeled using semi-empirical relations. For non-lifting geometries, look-up tables were created by running the
geometry in a commercial aerodynamic analysis tool. Once the aerodynamic model was integrated into PEACE, an
example case was demonstrated by sizing a tilt-wing configuration for a given design mission. The trade studies were
also possible by changing the wing geometry parameters because the embedded parametric aero-propulsive model
depends on the geometry alone. The corresponding results allowed the identification of an optimal wing geometry
for the given mission requirements and presented the trends in overall vehicle size with the change in performance
requirements like cruise speed and range.
Integrating a semi-empirical aero-propulsive model into the parametric sizing framework allows the designers to have
an initial aerodynamic estimate while creating the vehicle geometry. This becomes very useful in the conceptual phase of
design, where one can change the size and location of a geometry component in order to achieve the desired aerodynamic
characteristics with minimal to no wait time. Future work will include developing a parametric aerodynamic model
for non-lifting geometries and increasing the capabilities of the aerodynamic model for lifting surfaces. The lifting
surface model will be generalized to work with complex lifting surfaces such as with compound tapered and cranked
planforms. The interaction of the lifting and non-lifting geometries will be implemented. The application of the
parametric aero-propulsive model to perform structural, flight dynamics, and simulation studies, and optimization of an
aircraft will be explored. Developing a physical prototype by performing sizing based on the embedded aero-propulsive
model and calibrating the model against the flight test data is also another interesting venue for future research.
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Appendix A: Validation Studies
Fig. A1 Variation of aerodynamic coefficients with angle of attack (
𝛼
) for left canard based on wing exposed
area
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Fig. A2 Variation of aerodynamic coefficients with angle of attack 𝛼for left wing based on wing exposed area
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Fig. A3 Variation of aerodynamic coefficients with angle of attack
𝛼
for left horizontal stabilizer based on wing
exposed area
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Fig. A4 Variation of aerodynamic coefficients with angle of attack
𝛼
for all lifting surfaces based on wing
exposed area
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Fig. A5 Circulation (Γ)distribution over a straight tapered wing in absence and presence of other bodies
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Fig. A6 Comparison of results of trim solution for straight level flight using two aerodynamic model with
complete downwash
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Appendix B: Vehicle Weight Buildup
Table B1 Component weight breakdown of TW-02 Pangolin sized for different trip distances
Range (300 km) Range (400 km) Range (500 km)
Component Mass (kg)/ % - MTOM Mass (kg)/ % - MTOM Mass (kg)/ % - MTOM
Fuselage 386 / 9.53 396 / 8.98 406 / 8.46
Wing 420 / 10.36 468 / 10.61 520 / 10.84
Canards 15 / 0.36 17 / 0.39 20 / 0.42
Horizontal Stab 50 / 1.22 58 / 1.31 67 / 1.41
Vertical Stab 53 / 1.32 61 / 1.38 69 / 1.44
Landing Gear 216 / 5.32 230 / 5.22 245 / 5.10
Nacelles 103 / 2.54 111 / 2.53 124 / 2.58
Structures 1242 / 30.65 1341 / 30.42 1450 / 30.24
Turboshafts 518 / 12.80 550 / 12.48 583 / 12.15
Gearboxes 89 / 2.19 97 / 2.21 107 / 2.24
Generators 280 / 6.90 306 / 6.95 336 / 7.02
Props 314 / 7.76 362 / 8.21 401 / 8.37
Prop Motors 325 / 8.03 342 / 7.76 367 / 7.66
Fans 8 / 0.20 10 / 0.22 12 / 0.25
Fan Motors 1 / 0.03 1 / 0.03 4 / 0.08
Propulsion 1536 / 37.91 1668 / 37.85 1810 / 37.76
Systems 449 / 11.08 486 / 11.04 525 / 10.96
Empty Weight 3226 / 79.64 3495 / 79.31 3786 / 78.96
Fuel 275 / 6.77 365 / 8.29 458 / 9.56
Battery 42 / 1.04 46 / 1.05 50 / 1.05
Energy 317 / 7.81 412 / 9.34 509 / 10.61
Payload 500 / 12.34 500 / 11.35 500 / 10.43
Gross Weight 4043 / 100.00 4407 / 100.00 4794 / 100.00
Prop motors 6 x 272 kW 6 x 285 kW 6 x 307 kW
Fan motors 2 x 2.75 kW 2 x 2.81 kW 2 x 8.89 kW
Turboshaft 2 x 1076 kW 2 x 1179 kW 2 x 1299 kW
Gearbox 2 x 1065 kW 2 x 1167 kW 2 x 1286 kW
Generator 4 x 437 kW 4 x 479 kW 4 x 526 kW
Battery pack 1 x 508kW 1 x 557 kW 1 x 607 kW
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