Flight Performance Evaluation of the Flying-V

Full text

Flight Performance Evaluation of the Flying-V
Godert J. de Zoeten∗, Carmine Varriale†, Roelof Vos‡
Delft University of Technology, Delft, 2629 HS, The Netherlands
This study evaluates the flight performance of a Flying-V aircraft designed for transonic
passenger transport. The Flying-V is a disruptive aircraft configuration that has shown to
possess promising aerodynamic performance during preliminary design. It is compared to a
competitor aircraft reminiscent of the Airbus A350-1000, for the same thrust-to-weight ratio
and a similar number of passengers. The most common performance metrics for the take-off,
landing, climbing and cruise phases have been assessed using a modular flight mechanics
model. Take-off and landing performance are evaluated through flight simulation using a simple
Euler method, while climb and cruise performance are evaluated in trimmed, steady-state
conditions. Only instantaneous performance is available for the latter two phases. The Flying-V
outperforms its competitor for basically all investigated metrics. Take-off length is shorter,
mainly due to a larger tail strike attitude that reduces the minimum unstick speed. Service and
absolute ceiling are higher, and its superior lift-over-drag ratio results in a 21% increase in the
cruise range parameter. Landing field lengths are similar for both aircraft, but the Flying-V has
a significantly larger pitch angle during approach. This causes longer de-rotation length, and a
large obscured segment of the pilot’s vision which could be problematic during operations.
List of symbols
𝛼angle of attack, rad 𝐿aerodynamic lift, N
𝛽angle of sideslip, rad 𝑀Mach number
𝛾flight path angle, rad 𝑁number of elements
𝛿control surface deflection, rad RP range parameter
𝛿𝑇normalized throttle 𝑆reference area, m2
𝜂overall power plant efficiency SAR specific air range, m/kg
𝜃pitch angle, rad 𝑇thrust, N
𝜇friction coefficient TSFC thrust-specific fuel consumption, g/(N·s)
Λsweep angle, deg 𝑉airspeed, m/s
Θambient temperature ratio w.r.t sea level 𝑊weight, N
𝑎speed of sound, m/s
𝑏reference span, mSubscripts and superscripts
𝑐mean aerodynamic chord, m app approach
𝑔gravitational acceleration, m/s2cs control surface
ℎaltitude, m dd drag divergence
𝑝, 𝑞 , 𝑟 roll, pitch, yaw rate, rad/s lo lift-off
𝑡/𝑐thickness over chord ratio mg main landing gear
𝑥longitudinal position, m mu minimum unstick
Aaspect ratio ng nose landing gear
𝐷aerodynamic drag, N pax passengers
𝐽𝑖𝑖 moment or product of inertia, kg·m2sl sea level
𝐻calorific value of fuel, J/kg ts tail-strike
I. Introduction
Over the course of the last 50 years, the overall efficiency of the tube-and-wing aircraft configuration has improved by
100 percent [
1
]. But the progress in terms of efficiency gains has slowed over the course of time, and the conventional
∗MSc Student, Flight Performance and Propulsion Section, Faculty of Aerospace Engineering
†Assistant Professor, Flight Performance and Propulsion Section, Faculty of Aerospace Engineering, C.Varriale@tudelft.nl; AIAA Member.
‡Associate Professor, Flight Performance and Propulsion Section, Faculty of Aerospace Engineering, R.Vos@tudelft.nl; AIAA Member.
1

aircraft configuration is regarded to be approaching an asymptote in terms of overall efficiency with the Airbus A350
and Boeing 787 [
2
]. With the demand for air travel doubling approximately every 15 years [
3
] and increasing constraints
in terms of noise and pollution, engineers have started looking at unconventional aircraft configurations that are possibly
more fuel efficient than the conventional configuration.
The Flying-V is a tailless, V-shaped aircraft in which the passenger cabin is integrated in each wing. It was first
proposed in 2015 by Benad [
4
], and is shown in Figure 1. Designed for the same mission as the Airbus A350, the
Flying-V has a lower wetted-area-to-volume ratio, a higher effective span due to the tall winglets, and a lower structural
mass due to the lateral distribution of the payload. A three-member family of Flying-V airplanes has been designed
where constant-cross-section wing plugs are employed to extend or shrink the wing and cabin [
5
]. Compared to the
A350-1000, the Flying-V-1000 has shown a 15% reduction in maximum take-off mass and a 22% reduction in fuel burn
over a 15 400
km
range with a payload mass of 67 metric tonnes. This is in line with the earlier findings that showed the
potential of a 25% improvement in aerodynamic efficiency along with a 15% reduction in the FEM-mass-to-takeoff-mass
ratio[2, 6].
Fig. 1 Rendering of the Flying-V aircraft.
While these studies showed promising results in terms of energy efficiency, they also sparked many research
questions. One line of research has concentrated on the control and handling qualities of the airplane. A 4.6%-scale
flight-test article was designed and built to measure the dynamic properties of the airplane. A half-model of the same
size was first experimentally examined in the wind tunnel. Based on wind tunnel tests, Palermo and Vos [
7
] showed that
the sub-scale model develops a strong pitch-up moment above an angle of attack of 20
deg
. Viet showed that the highly
swept wing develops a complicated vortex pattern that changes with the angle of attack [
8
]. Subsequent aerodynamic
analysis using large-eddy simulations revealed that both the pitch break and the vortex formation are sensitive to the
flight Reynolds number, and are suppressed to angles of attack in excess of 30 deg.
To derive the aerodynamic model of the sub-scale airplane, system identification techniques were applied to the wind
tunnel experiments as well as the flight tests, with excellent correlation between the two [
9
,
10
]. These tests showed that
the airplane is naturally stable in all modes. This confirmed the findings of a separate study performed by Cappuyns,
who numerically evaluated the handling qualities of the full-scale Flying-V using a vortex-lattice model to represent the
aerodynamic behavior of the model [
11
]. This model was subsequently used in experiments in a flight simulator to
score the handling qualities on a Cooper-Harper rating [
12
,
13
]. These studies demonstrated that the Flying-V has Level
1 handling qualities across the majority of the flight envelope.
In this paper, the flight performance of the Flying-V is compared to the one of the Airbus A350. The overall
research question that is answered is: how does the flight performance of the Flying-V compare to the Airbus A350,
provided both airplanes have an identical thrust-to-weight ratio? The overall flight performance comprises four different
parts: landing performance, take-off performance, climb performance and cruise performance. For each of these parts,
appropriate metrics are defined to compare the flight performance aspects. A flight mechanics analysis is employed to
simulate the performance of either airplane during each of these flight phases. Both newly generated data and data from
earlier studies are used to populate the various models that underpin the flight mechanics analysis.
The remainder of the is paper is structured as follows. Section II presents the disciplinary models that function as
a basis for the flight mechanics model: the reference geometries, aerodynamics, propulsive units, contact forces and
2

landing gear, and mass distribution. Then, section III presents how the various flight maneuvers have been modelled
and evaluated within the context of a simple flight simulation framework. In section IV, the predictions of the flight
mechanics model for the landing and take-off performance of the Airbus A350 are compared to the corresponding data
available in the open literature. The evaluation of the flight performance of the Flying-V, with comparison to the A350,
is subsequently presented in section V. Lastly, section VI presents the conclusions of this study and provides possible
avenues for further research.
II. Flight mechanics model
This section presents the flight mechanics model employed to analyze the flight performance of both aircraft under
investigations: the Flying-V-1000 and the Airbus A350-1000. The following subsections describe each aspect of the
overall flight mechanics model in more detail. The top-level architecture of the complete model is presented in Figure 2.
Fig. 2 Block-scheme of the flight mechanics model employed for both aircraft under investigation.
Table 1 shows the input specifications that have been used for this comparison study. The Flying-V-1000 has been
designed for a similar passenger capacity and Payload Mass (PLM) as the A350-1000. In light of its unconventional
geometry, it is able to obtain an 18% reduction in Maximum Take-off Mass (MTOM) with respect to its competitor, as
found by a previous study on the Flying-V family [
5
]. According to another study on the structural characteristics of
the Flying-V, its Operating Empty Mass (OEM) is about 32% lower than the competitor [6]. The fraction between the
Maximum Landing Mass (MLM) and the MTOM of the Flying-V has been assumed to be the same as the one of the
A350-1000. Moreover, the thrust-to-weight ratio of both aircraft has also been assumed to be the equal for both aircraft.
With these assumptions, it is expected that the flight performance differences that are to be found can be attributed
exclusively to the difference in aerodynamic characteristics and mass properties.
Table 1 Top-level specifications for both aircraft under investigation.
Flying-V-1000
[5, 6]
Airbus A350-1000
[14, 15]
𝑁pax 361 366
PLM 67 000 kg 67 000 kg
MTOM 259 000 kg 316 000 kg
MLM 193 000 kg 236 000 kg
𝑇max 707 kN 863 kN
𝑇/𝑊0.278 0.278
3

A. Geometry
The wing planform of the Flying-V-1000 as designed by Oosterom [
5
] and the one of the Airbus A350-900 have been
used to generate the aerodynamic datasets necessary for flight simulation. A planform comparison between the two
reference models is shown in Figure 3a. Figure 3b shows the position and role of all movable devices employed for each
aircraft.
a) Planform comparison
Droop Nose Device
Slats
Flaps Elevator
Elevator
Elevon
Elevons
Rudder
Rudder
b) Control surfaces positions and sizes
Fig. 3 Comparison among reference plan forms of the Airbus A350-900 and Flying-V-1000, with control location and role of movable devices.
Since the aerodynamic dataset is generated by a Vortex Lattice Method (VLM), as illustrated in the following section,
it is deemed acceptable to use the A350-900 reference geometry to derive a dataset for the A350-1000. The two aircraft
employ the same main wing and empennage, but the A350-1000 has a slightly larger winglet than the -900 version. The
moment arm of the empennage with respect to the center of gravity has been increased by 6
.
98 m to take into account
the extra fuselage length of the A350-1000. Similarly, the reference point for the reduction of all moments has been
shifted backwards by 3.81 m to account for the different position of the wing.
Over-the-wing spoilers, not reported in the figures, are assumed to be employed exclusively for breaking on the
runway. In this phase, the deflection of spoilers increases both the aerodynamic drag and the down-force on the main
landing gear. As the latter increases, the maximum braking force that can be applied without skidding also increases,
hence allowing for a further reduction of the required braking distance to standstill on the runway. The landing gear
dimensions of the Flying-V have been obtained from [
16
], using the “Floor 5.5” configuration. The corresponding pitch
angles for tail-strike have also been retained for this study. The top-level geometric characteristics of the two aircraft
have been reported in Table 2.
B. Aerodynamics
Aerodynamic actions and derivatives due to the airframe and movable devices are expressed as a function of the angle
of attack
𝛼
and asymptotic Mach number
𝑀
, and are linearly proportional to the angle of sideslip
𝛽
, body angular
rates
𝑝, 𝑞 , 𝑟
and control surface deflections
𝜹
. Such baseline aerodynamic model is expressed in Equation 1 for a
generic action (force or moment) coefficient 𝐶𝐹. All actions are expressed in body axes through data tables which are
interpolated linearly at run-time.
𝐶𝐹(𝛼, 𝑀 , 𝛽, 𝜔, 𝛿cs)=𝐶𝐹0(𝛼, 𝑀) + 𝜕𝐶𝐹(𝛼, 𝑀 )
𝜕𝛽 𝛽+
𝜔=𝑝,𝑞,𝑟
𝜕𝐶𝐹(𝛼, 𝑀)
𝜕𝜔 𝜔+
𝑁cs

𝑖=1
𝜕𝐶𝐹(𝛼, 𝑀)
𝜕𝛿𝑖
𝛿𝑖(1)
For the dataset of the A350, the
𝐶𝐹0
term contains aerodynamic actions due to the airframe in take-off, landing and
cruise configurations. The Flying-V does not incorporate high-lift devices.
4

Table 2 Top-level geometric characteristics of both aircraft under investigation.
Parameter Flying-V-1000 Airbus A350-1000
𝑏65 m 65 m
𝑆883 m2462 m2
A4.78 9.15
𝑐18.74 m 9.48 m
Λ𝑐/455.8 deg 29.6 deg
𝑡/𝑐0.1299 0.1036
𝜃ts 19.2 deg 10.0 deg
𝑥mg 31.8 m 37.1 m
𝑥ng 6.47 m 4.63 m
The numerical database underlying such model has been generated using the Odilila VLM. This software has
been developed by Airbus, and its predictions of lift curve slopes and induced drag have been verified in previous
research studies [
6
,
11
]. As all VLMs, Odilila assumes incompressible, inviscid and irrotational flow, and is therefore
inherently limited. Thickness and viscosity effects are also absent, together with non-linear aerodynamic behaviors.
These limitations justify the adoption of a slightly inaccurate geometry, as mentioned in the previous section, but also
necessitate awareness in the modeling and interpretation of certain performance.
In order to avoid operating in a non-linear aerodynamic regime, a maximum usable angle of attack of
𝛼max =
20
deg
has been imposed for all flight simulations of the Flying-V, in light of the pitch-up break tendencies that have been
discovered through wind tunnel experiments [
7
]. For the A350-1000, such limit has been instead assumed to be 15
deg
.
To account for thickness, viscosity and interference effects, the baseline aerodynamic dataset from Odilila has been
enhanced with a semi-empirical, component-based zero-lift drag model [
17
,
18
]. For the wings, fuselage, nacelles and
pylons, the zero-lift drag coefficient is calculated using the flat plate skin-friction coefficient
𝐶𝑓
, a form factor
𝑓
to
account for wave drag, an interference factor 𝑄and the wetted area of the component 𝑆wet, according to Equation 2.
𝐶𝐷0=𝐶𝑓𝑓 𝑄𝑐
𝑆wet
𝑆(2)
Estimated zero-lift drag contributions in take-off, touch-down and cruise conditions are reported in Table 3a. Figure 4
shows the aerodynamic efficiency and lift curves of the Flying-V and Airbus A350 in subsonic and transonic regimes.
In the event of an engine failure, the additional drag due to a blocked rotor or windmilling engine are also modelled
using empirical relations [
18
]. It is assumed that the zero-lift drag does not contribute to the aerodynamic moments
about the aircraft Center of Gravity (CG), except for in the case of the failed engine and the landing gear. For the latter,
separate strut and wheel drag coefficients have been determined, and drag forces are assumed to be applied at the middle
of the strut and at the centre of the wheel, respectively. Moment contributions due to these drag forces are calculated
and added to the external aerodynamic moments, after appropriate transformation to the body reference frame.
An empirical model based on the “Delta Method” has been implemented to account for transonic wave drag [
19
,
20
].
As shown in Equation 3, the three-dimensional drag divergence number
𝑀3D
dd
has been estimated for both aircraft on the
basis of its two-dimensional counterpart
𝑀2D
dd
, depending on airfoil characteristics, and corrected for quarter-chord
sweep angle and aspect ratio of the wing.
𝑀3D
dd =𝑀2D
dd +Δ𝑀Λ𝑐/4+Δ𝑀
A(3)
The average quarter-chord sweep angle and thickness-to-chord ratio presented in Table 2 have been used for the wave
drag computations. The resulting three-dimensional drag divergence number are reported in Table 3b. The Flying-V has
a larger
𝑀3D
dd
than its competitor due to the benefits of a large sweep angle and a small aspect ratio. Although the Delta
method data includes a wide range of aircraft with sweep angles up to 60 degrees and aspect ratios as low as 4.7, it must
be noted that none of the investigated aircraft was a flying wing. Therefore it is not known whether this method could
also be accurately applied to this unconventional aircraft configuration. For the A350-1000 the fuselage wave drag has
also been accounted for, although its contribution is small.
5

The deflections of over-the-wing spoilers are assumed to have only effect on the change in lift coefficient, while their
effect on drag has been neglected. This is to avoid giving the Flying-V an unfair advantage when comparing braking
performance, since its model for drag due to spoilers needs to be further verified. For the Flying-V, it is assumed that the
change in lift coefficient due to spoiler deflection is
Δ𝐶𝐿=−
0
.
16, on the basis of previous research [
21
]. For the Airbus
00.511.522.5
5
10
15
20
25
Flying-V
A350
𝐶𝐿
𝐿/𝐷
𝑀=0.85
𝑀=0.25
a) Lift over drag ratio
−50510 15 20
−0.5
0
0.5
1
1.5
2
2.5
Flying-V
A350
𝛼(deg)
𝐶𝐿
𝑀=0.85
𝑀=0.25
b) Lift curve
Fig. 4
Clean aerodynamics of the Flying-V-1000 and Airbus A350-1000 in subsonic and transonic regimes. All drag contributions included. All
movable devices and landing gear retracted.
Table 3 Corrections to the baseline aerodynamic dataset based on semi-empirical models.
(a) Zero-lift drag coefficient per component in various flight phases
Δ𝐶𝐷0
Component
Flying-V-1000 Airbus A350-1000
Take-off Landing Cruise Take-off Landing Cruise
Fuselage - - - 48.9 50.5 46.1
Wings 62.9 64.0 61.2 94.9 99.6 89.4
Nacelles 6.5 6.6 6.3 14.2 14.9 13.4
Pylons 3.5 3.5 3.4 5.3 5.5 5.0
Leakage 4.4 4.4 4.4 8.0 8.0 8.0
Flaps - - - 68.5 205.4 -
Landing gear 50.5 50.5 - 80.0 80.0 -
(b) Maximum angle of attack, drag-divergence Mach number, and Δ𝐶𝐿due to over-the-wing spoiler deflections
Flying-V-1000 Airbus A350-1000
𝛼max 20 deg 15 deg
𝑀3D
dd 0.961 0.867
Δ𝐶𝐿−0.16 −0.13 −0.34(𝛿flap /30)
6

A350-1000, it is a function of the flap deflection angle:
Δ𝐶𝐿=−
0
.
13
−
0
.
34
(𝛿flap/
30
)
. The latter model has been
formulated on the basis of available data from the Boeing 747. This is deemed acceptable, since force coefficients are
normalized with respect to the wing reference area, and the planform of the A350-1000 and B747 are overall comparable
at the fidelity level adopted for this study.
C. Propulsion
Both the Flying-V and the reference aircraft employ two high-Bypass Ratio (BPR) engines, comparable to the Rolls
Royce Trent XWB [
14
]. The engines locations have been taken from [
22
] and [
14
] for the Flying-V and Airbus A350,
respectively. A semi-empirical thrust lapse model based on engine data of two-shaft turbofan engines is used to predict
the available thrust and
TSFC
for different altitudes, Mach numbers, and flight phases [
23
]. Such model is shown in
Figure 5a for a turbofan engine with BPR =10 and a Static Sea-Level (SSL) thrust equal to 𝑇SSL =353 kN.
In the present work, the model for maximum available thrust during take-off is going to be used for flight conditions
at
𝑀 <
0
.
4and
ℎ <
1
km
. In all other flight conditions, the thrust lapse for the climb phase is used. The resulting
maximum available thrust predicted by this merged model as a fraction of the SSL thrust is shown in Figure 5b.
a) Thrust lapse models for take-off and climb phases b) Merged thrust lapse model
Fig. 5
Maximum available thrust as a fraction of the SSL thrust as a function of Mach number and altitude, for a turbofan engine with
BPR =
10 and
𝑇SSL =353kN.
The specific fuel consumption is calculated as a function of altitude and Mach number using the following Equation 4,
TSFC =TSFCref Θ
Θref 𝑀
𝑀ref 𝑛
(4)
where
Θ
is the ambient temperature ratio with respect to sea level temperature [
23
]. The reference
TSFC
, temperature
ratio and Mach number are the respective values in cruise conditions. The same reference values have been chosen
for both aircraft. A value of
TSFCref =
13
.
5 g
/(kN ·
s
)
is assumed, which corresponds to the one of the Airbus
A350-1000 [
24
]. The reference Mach number is assumed to be 0
.
85, and the reference altitude 11
km
. The exponent
𝑛
is engine-specific, and has been estimated to be equal to 0.42 [23].
The overall power plant efficiency is expressed as in the following Equation 5 [
25
], where
𝐻
is the calorific value of
the fuel. The latter has been assumed to be equal to 43.2 MJ/kg for both aircraft.
𝜂=𝑎sl
𝐻/𝑔
𝑀
TSFC/√Θ(5)
D. Contact forces
Contact between the runway and each landing gear is established on the basis of the current position and attitude of
the aircraft. When the wheels of either the main or nose landing gear make contact with the runway, two additional
7

types of forces are modeled: a reaction force normal to the runway, and a friction force parallel to the runway. The
friction force is parallel to the runway and proportional to the normal force through a friction coefficient 𝜇.
Only longitudinal-symmetric flight is considered in all flight phases involving ground contact forces. During ground
contact, it is assumed that the contact forces between the runway and the landing gear wheels are able to counteract
excess yawing and rolling moments, as well as side forces. The normal reaction forces and the friction forces are
calculated at every time-step by assuming that the aircraft is instantaneously in static equilibrium. Actions due to inertial
accelerations are therefore neglected. This is an important limitation of the chosen approach for the absolute estimation
of the performance of each aircraft, but the comparison between the two aircraft performance remains fair.
Braking is modelled by simply adjusting the friction coefficient of the wheels of the main landing gear. The rolling
friction coefficient is assumed to be
𝜇mg =
0
.
02 for a dry concrete runway [
26
]. When brakes are applied, a braking
coefficient is assumed to be constant and equal to 𝜇mg =0.4[21].
E. Inertia and Center of Gravity
The inertia tensor used in the present research has been estimated through a structural analysis of the Flying-V-1000
and A350-900 [
6
]. The moments of inertia of the Airbus A350-1000 have then been estimated by correcting the
A350-900 values for the mass and geometric differences between the -900 and -1000 models. Aircraft mass is assumed
to be distributed symmetrically about the x-axis, hence the
𝐽𝑥𝑦
and
𝐽𝑦𝑧
products of inertia are assumed to be zero. The
𝐽𝑥𝑧
product is neglected, as it can be expected to be very small compared to the principal moments of inertia. Numerical
values for both aircraft are presented in Table 4a.
The range of CG locations that can be used by the Flying-V has also been found in previous research [
11
]. The
foremost CG location is the one that allows to obtain a load factor of 1
.
3
𝑔
with a pull-up maneuver in approach conditions.
The aftmost CG location was determined by imposing a static margin of 2.5%. For the Airbus A350-1000, the CG
limits are taken from the corresponding Aircraft Characteristics and Maintenance Planning (ACAP) manuals [
14
]. The
usable CG range of both aircraft is reported in Table 4b, in terms of the Mean Aerodynamic Chord (MAC).
Table 4 Moments of inertia and CG limits of both aircraft under investigation.
(a) Moments of inertia around the aircraft body principal axes.
Flying-V-1000 Airbus A350-1000
MTOM OEM MTOM OEM
𝐽𝑥 𝑥 /106kg·m239.6 12.2 31.8 9.4
𝐽𝑦𝑦 /106kg ·m227.6 10.5 50.8 28.2
𝐽𝑧𝑧 /106kg ·m265.8 21.4 86.4 37.4
(b) Usable CG range for stability and controllability
Flying-V-1000 Airbus A350-1000
𝑥le
𝑐20.94 m 31.75 m
𝑥fore
CG 0.45𝑐0.18𝑐
𝑥aft
CG 0.57𝑐0.43𝑐
Δ𝑥CG 0.12𝑐0.25𝑐
III. Methodology
The Performance, Handling Qualities and Load Analysis Toolbox (PHALANX) has been used to integrate an
aerodynamic, a weight and balance, and a propulsion module into a complete flight mechanics model, which can be
employed to perform 6-Degree of Freedom (DoF) flight simulation. The toolbox has been developed in-house in
MATLAB, using the Simulink and Simscape multi-body dynamics packages. It has already been implemented in
several other research applications to unconventional aircraft configurations [
27
,
28
], including studies on the propulsive
empennage concept [
29
], and the trim and transient response of staggered box-wing aircraft [
30
,
31
]. A top-level
overview of the PHALANX flight simulation toolbox is shown in Figure 6.
The following subsections present in more detail the methodology adopted to simulate flight dynamics and calculate
flight performance, and illustrate the approach adopted to model different flight phases.
A. Flight dynamics simulation
Flight dynamics is simulated by summing the force and moment contributions due to the airframe aerodynamics, the
propulsion system, ground contact forces, and inertial loads in the aircraft body reference frame. These contributions
depend on model states as well as on the control inputs provided by a pre-implemented pilot model, and/or calculated
8

Fig. 6 Top-level overview of the PHALANX flight simulation toolbox.
through a simple FCS (FCS). State propagation is achieved, in this particular study, through a forward Euler scheme.
The angle of attack and angle of sideslip are calculated at each time-step from the airspeed components in body axes.
The aircraft is trimmed by prescribing initial values of altitude, airspeed, sideslip angle and Euler angular rates.
Either the flight path angle
𝛾
or the throttle level
𝛿𝑇
can be additionally specified to further constrain the formulation of
the trim problem. Trim is achieved by finding the combination of pilot inputs on the stick and Euler angles that minimize
the norm of an array containing the aircraft linear and angular accelerations, together with the error in the prescribed
sideslip angle. If trim is required for a longitudinal-symmetric flight condition, the pilot inputs on the lateral-directional
axes, as well as the roll and yaw attitude angles are automatically set to zero, and the trim problem is greatly simplified.
In all cases, the solution is found with an iterative, gradient-based optimization algorithm, and is therefore locally
optimum [31].
The FCS involves an open-loop pilot model and the possibility to implement different types of closed-loop controllers.
Movable surfaces are controlled by (auto-)pilot inputs for the roll, pitch and yaw axes, and the throttle setting
𝛿𝑇
.
Actuators are assumed to be ideal, with a deflection limit of 30
deg
. With reference to Figure 3b, the A350 employs the
elevator for pitch control, the rudder for yaw control and the elevons exclusively for roll control. The Flying-V employs
both the elevon and elevator for pitch control, while the elevon and rudder are used for roll and yaw control, respectively.
Different PID controllers are implemented to perform certain maneuvers, as explained briefly in the following sections.
B. Take-off
The take-off maneuver begins at standstill and ends when the lowest point of the aircraft surpasses the screen height
ℎscreen =
35
ft
[
32
]. The maneuver is simulated using 2D equations of motion, restricting the evolution of the aircraft to
be symmetric in the vertical plane. The runway is assumed to be horizontal (
𝛾=
0). The aircraft uses its maximum
available thrust at full throttle (𝛿𝑇=1), and each engine spools up/down with a characteristic time of 5.0 s.
The aircraft initiates rotation about the contact point of the main landing at a certain speed
𝑉R
. The optimal value of
𝑉R
is determined for a given aircraft model via an iterative search algorithm with an accuracy of 0
.
5 m
/
s. During the
first part of the rotation phase, a reference pitch rate
𝑞ref
is targeted, until the angle of attack reaches an assigned value
𝛼ref
. This value is assigned arbitrarily to minimize overshoot in the following part of the rotation phase. Once
𝛼ref
has
been reached, a reference pitch angle
𝜃ref
is targeted. The reference value is assigned for each aircraft model on the
basis of the tail-strike angle, reported in Table 2: 𝛼ref =𝜃ts −0.5 deg.
If One Engine Inoperative (OEI) conditions occur before the decision speed
𝑉1
, the take-off procedure is aborted. In
such a scenario, the following operations are simulated:
1) 2.9 s after the engine failure, the friction coefficient of the main landing gear is updated to its braking value;
2) 3.3 s after the engine failure, the failed engine is cut-off from the FCS;
3) 4.3 s after the engine failure, over-the-wing spoilers are fully deployed to act as speed bakes.
The aforementioned time delays have been introduced to take into account typical human behavior during the
corresponding operations [
33
]. An additional controller deflects control surfaces over the main wing to maximize the
loading on the main landing gear while retaining at least 8% of the aircraft weight on the nose wheel. This is in order to
allow the pilot to maintain directional control of the aircraft [17, 18].
9

If the OEI condition occurs after the decision speed
𝑉1
, the take-off procedure is continued. In such a case, as soon
as the nose wheel loses contact with the ground, an automatic controller calculates the rudder deflection required to
neutralize the yawing moment due to thrust imbalance. Such deflection is used exclusively to account for its additional
aerodynamic drag, but every other force and moment is disregarded. In other words, it is assumed that the aircraft is
always able to maintain its straight trajectory on the runway. On the other hand, it can be expected that the predicted
take-off distance in OEI conditions are slightly underestimated, since the airborne phase does not include sideslipping
flight or a banking angle.
C. Landing
Like for the take-off maneuver, landing is simulated using 2D equations of motion, and only longitudinal-symmetric
flight is considered. The landing maneuver begins with the aircraft being trimmed at a screen height of 50
ft
, with a
flight path angle
𝛾=−
3
deg
, at an assigned approach speed
𝑉app
. The approach speed is assumed to be equal to 1.23
times the stall speed in landing configuration [
32
]. It has been calculated using the available aerodynamic model at SSL
and MLM conditions. For the Flying-V, 𝑉app =74.6 m/s, while for the A350, 𝑉app =75.6 m/s
Until the aircraft altitude is greater than 1 m above ground, a simple autopilot uses the elevators to target a reference
touch-down descent rate equal to 1
.
83 m
/
s, which is the recommended outcome of a standard flare maneuver [
32
]. For
the two aircraft under investigation, this value corresponds to a flight path angle approximately equal to
𝛾ref =−
1
.
4
deg
.
Additionally, engine thrust is reduced to idle, while taking the aforementioned spool time into account.
After touching down, de-rotation is initiated by targeting a reference pitch rate
𝑞ref =−
3
deg/
s. Once the nose-wheel
contacts the runway, braking is simulated by updating the value of the friction coefficient of the main gear, deploying the
over-the-wing spoilers as speed brakes, and deflecting control surfaces to maximize the load on the main landing gear.
This procedure is identical to the one described in the previous III.B for an aborted take-off.
D. In flight phases
During the climb and cruise phases, the 3D equations of motion are used to trim the aircraft in different flight conditions.
No dynamic simulation is performed in these flight phases, hence the estimated performance should be interpreted as
quasi-steady. Asymmetric flight conditions and non-zero side-slip angles are also considered in case of OEI conditions.
The landing gear is assumed to be retracted, and all its contributions are therefore null.
For the cruise phase, attention is focused on the maximum Specific Air Range (
SAR
).
SAR
is the range covered
per unit of fuel consumed, and is defined in the following Equation 6, where
𝜂
is the overall power plant efficiency,
introduced in Equation 5.
SAR =𝑉
𝑇·TSFC =𝐻
𝑔
1
𝑊𝜂𝐿
𝐷(6)
The instantaneous
SAR
is inversely proportional to the aircraft weight and, in the most general case, directly
proportional to the Range Parameter
RP
, defined in the following Equation 7. In light of the expression of
𝜂
and the
chosen model for
TSFC
, this parameter is proportional to the product between the aerodynamic efficiency and the Mach
number elevated to a power lower than one. This choice results in the fact that no propulsive parameter has any impact
on the cruise performance evaluation.
RP =𝜂𝐿
𝐷∝𝑀1−𝑛𝐿
𝐷(7)
Alternatively, if
TSFC
was to be assumed to be constant across the flight envelope, the
RP
would be proportional to the
transonic efficiency
𝑀 𝐿/𝐷
[
25
]. If the overall efficiency
𝜂
was assumed to be constant altogether, the range parameter
would be simply proportional to the aerodynamic efficiency 𝐿/𝐷.
IV. Validation
To validate the fidelity of the overall flight mechanics model and adequacy of the developed methodology, the predicted
take-off and landing distances of the A350-1000 are compared to reference data extracted from the ACAP report [14].
A series of landing simulations have been performed for the A350-1000 model, in SSL conditions, at MLM with
different positions of the CG. The resulting landing field lengths range from 2112 m to 2153 m, and have been compared
to a reference landing distance of approximately 2100 m. The latter has been calculated by dividing the measured
landing distance provided in the ACAP report by 0.6, as prescribed by the Federal Aviation Regulations [34].
10

A series of take-off simulations have been performed for different aircraft weights and at different altitudes. The
reference values reported in the ACAP model have been assumed to be equal to 115% of the measured take-off distance,
as prescribed by Certification Specifications [
32
]. Hence, the measured take-off lengths from simulations have been
scaled up accordingly. The comparison between the estimated runway lengths and the updated reference values is shown
in Figure 7. The flight mechanics model seems able to predict take-off runway lengths reasonably well for altitudes up
to about 610 m, while the calculated runway lengths seems to be under-predicted at altitudes of approximately 1220 m.
Despite limited, the validation process is regarded as satisfactory. The results are believed to be sufficiently
accurate to justify the use of the developed flight mechanics model and methodology for the purpose of comparing the
performance of the A350-1000 and Flying-V-1000 aircraft models.
Take-off runway length (m)
Fig. 7
Validationof take-off runway length for the A350-1000 with reference
data extracted from the ACAP [14].
V. Results
This section presents the flight performance of the Flying-V-1000, with comparison to the one of the Airbus A350-1000.
Classic performance metrics related to the four main mission phases of take-off, landing, climb and cruise are presented
and discussed in the corresponding sub-sections.
A. Take-off performance
In accordance with CS25.113, the take-off distance has been calculated as 115% of the horizontal distance along the
take-off path, with all engines operative, from standstill to the point where the aircraft is 35
ft
above the runway [
32
].
The minimum take-off distance of both aircraft is reported in Figure 8a for different altitudes and MTOM fractions, and
with the CG at its forward limit position. On average, the Flying-V-1000 achieves a take-off distance 25% shorter than
the A350-1000, with such difference increasing with increasing mass and altitude. This is to be attributed to the fact
that the the Flying-V-1000 has:
•a lower absolute MTOM than its competitor (Table 1);
•
a much larger reference area, despite a lower lift-slope, which allows it to obtain comparable lift to its competitor,
for a given angle of attack (Table 2, Figure 4b);
•
a much larger tail-strike attitude, which allows it to achieve greater angles of attack during the ground run
(Table 2);
These three conditions result in the minimum unstick speed
𝑉mu
of the Flying-V-1000 being significantly lower than for
the A350-1000, as shown in Figure 8b.
The take-off distance breakdown of the two aircraft is compared in Figure 9, for different CG positions, at SSL
and MTOM. For both aircraft, the total take-off distance decreases as the CG shifts rearwards. This is mainly due to a
11

a) Takeoff distance b) Minimum unstick speed
Fig. 8
Minimum take-off distance and corresponding minimum unstick speed of the Flying-V-1000 and the Airbus A350-1000, for different altitudes
and MTOM fractions. CG is at the respective forward limit position for each aircraft.
FWD MID AFT
CG Position
0
500
1000
1500
2000
2500
3000
Take-off distance (m)
Pre-rotation
FWD MID AFT
CG Position
0
500
1000
1500
2000
2500
3000
Pre-rotation
Rotation
Rotation
Airborne
Airborne
Airbus A350-1000
Take-off distance (m)
a) Flying-V-1000
Flying-V-1000
FWD MID AFT
CG Position
0
500
1000
1500
2000
2500
3000
Take-off distance (m)
Pre-rotation
FWD MID AFT
CG Position
0
500
1000
1500
2000
2500
3000
Pre-rotation
Rotation
Rotation
Airborne
Airborne
Take-off distance (m)
b) Airbus A350-1000
Fig. 9 Take-off distance breakdown comparison between the Flying-V-1000 and A350-1000, for varying CG positions, at SSL and MTOM.
decrease in distance during the rotation phase. The Flying-V-1000 features a larger decrease in take-off distance over the
entire CG range, indicating that the CG position has a larger influence on the optimal
𝑉𝑅
for the Flying-V-1000 than for
the A350-1000. This could be expected, since the CG range of the Flying-V-1000 is closer to the longitudinal position
of the main landing gear.
In particular, the most rearward CG position of the Flying-V almost coincides with the position of the main landing
gear, while the most rearward CG position of the A350-1000 lies about 1
.
3 m ahead of its main landing gear. Since the
moment arm of the aircraft weight with respect to the main landing gear is much smaller for the Flying-V-1000 than
for the A350-1000, it is possible to rotate the nose of the aircraft upwards at an earlier speed for the former. On the
other hand, the absolute distance covered during the rotation phase is lower for the A350-1000, on average. This is
mostly due to the fact that the rotation phase starts at a higher speed for the latter. Finally, the airborne distance of the
Flying-V-1000 is shorter for all CG positions. This is due to a lower lift-off speed, and a larger climb angle at lift-off as
12

0.7 0.75 0.8 0.85 0.9 0.95
1
MTOM fraction
60
65
70
75
80
85
90
95
Airspeed (m/s)
Flying-V-1000
Airbus A350-1000
a) Decision and take-off speeds
0.7 0.75 0.8 0.85 0.9 0.95
1
MTOM fraction
0
500
1000
1500
2000
2500
3000
3500
4000
Balanced Field Length (m)
Flying-V-1000
Airbus A350-1000
b) Balanced Field Length (BFL)
Fig. 10
Performance parameters of the Flying-V-1000 and the Airbus A350-1000 for the OEI take-off maneuver, for different MTOM fractions. CG at
forward limit in SSL conditions.
compared to the A350-1000.
Figure 10 compares the main performance parameters related to a take-off maneuver in OEI conditions. All of the
reported parameters are found by simulating the failure of an engine at an assigned speed during the ground run, and
simulating both a continued take-off and an aborted take-off after such event. The decision speed
𝑉1
and the take-off
speed
𝑉2
at the screen height are found when the distances for continued and aborted take-off are equal. By definition,
such distance is the Balanced Field Length (BFL).
The figure shows that both the reference speeds and the BFL of the the Flying-V-1000 are significantly lower than
the ones of the A350-1000. This is mostly caused to the different position of the engines within each aircraft. Due to the
over-the-wing position of the engines for the Flying-V, an engine failure results in a pitch-up tendency of the aircraft
with respect to the all-engines-operative condition. It is then easier to initiate rotation with OEI for the Flying-V-1000
rather than for the A350, with its engines installed under the wing. Lastly, the decision and take-off speeds uniformly
decrease by about 2–2.5% when shifting the CG to its rearward limit position. The same occurs for the BFL.
B. Landing performance
A comparison between the landing distance breakdown of the Flying-V-1000 and A350-1000 is shown in Figure 11.
The two aircraft have comparable total landing distance for all positions of the CG, but a different repartition of distance
covered in the three main phases of the landing maneuver. During the airborne phase, the A350-1000 covers a slightly
larger distance than the Flying-V-1000. This is due to the slightly higher approach speed of the A350, which additionally
requires a more extended flare maneuver to reduce the descent rate at touchdown.
During the de-rotation phase, the A350 covers much less distance than the Flying-V. This is because the latter has a
higher pitch attitude at touchdown and a lower pitch attitude when resting on the ground (
𝜃=−
3
deg
), and the maneuver
is simulated with the same imposed de-rotation pitch rate for both aircraft. For both aircraft it can be seen that the
de-rotation distance decreases as the CG shifts rearwards, since this determines a lower pitch attitude at touchdown. For
the Flying-V-1000 this effect has a larger impact on the landing distance than for the A350-1000.
In the braking phase, the Flying-V requires a much shorter distance until standstill than the A350. This is ascribable
to the fact that it is able to generate a much grater aerodynamic load on the main lading gear, and can be justified by two
factors. Firstly, the Flying-V-1000 has no high-lift devices and a ground attitude of
𝜃=−
3
deg
. On the runway (
𝛾=
0),
this results in the airframe naturally generating down-force on the main landing gear. Secondly, despite both aircraft
use spoilers for lift dumping, the Flying-V is able to deflect all of its trailing-edge control surfaces, as opposed to only
the tail elevator of the A350. The time history of the total load on the main landing gear during landing is reported in
Figure 12a, while the time history of the aircraft deceleration is shown in Figure 12b.
Due to its highly swept wing and the absence of high lift systems, the Flying-V-1000 requires a larger landing pitch
13

FWD MID AFT
CG Position
0
200
400
600
800
1000
1200
1400
Landing distance (m)
FWD MID AFT
CG Position
0
200
400
600
800
1000
1200
1400
Airborne Airborne
De-rotation
Braking Braking
Airbus A350-1000
De-rotation
a) Flying-V-1000
FWD MID AFT
CG Position
0
200
400
600
800
1000
1200
1400
Landing distance (m)
FWD MID AFT
CG Position
0
200
400
600
800
1000
1200
1400
Airborne Airborne
De-rotation
Braking Braking
Landing distance (m)
Flying-V-1000
De-rotation
b) Airbus A350-1000
Fig. 11 Landing distance breakdown comparison between the Flying-V-1000 and A350-1000, for varying CG positions, at SSL and MLM.
0 5 10 15 20 25
Time (s)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
CG middle
CG fore
CG aft
Flying-V-1000
Airbus A350-1000
a) Total load on the main landing gear
0 5 10 15 20 25
Time (s)
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
Acceleration /g
Airbus A350-1000
Flying-V-1000
CG middle
CG fore
CG aft
b) Aircraft deceleration
Fig. 12 Time histories comparison of total load on the main gear wheels and aircraft deceleration during landing, for different positions of the CG.
angle than the A350-1000. Time histories of the pitch angle of both aircraft during landing are shown in Figure 13a.
During the flare maneuver, the pitch angle is increased even more to reduce the descent rate, and this may become
problematic for the pilots to have a clear view of the runway. Figure 13b shows the time history of the obscured segment
during landing. This is the horizontal distance to the closest point on the ground that the pilot can see, in light of the
aircraft attitude and nose geometry [
35
]. The pilot’s eye is assumed to be located 1
.
87 m behind the nose and 1
.
00 m
above the aircraft centre line, while the over-nose angle of the cockpit is assumed to be 25
.
7
deg
for the Flying-V-1000
and 20
deg
for the A350-1000 [
14
]. For both aircraft, it can be seen that the landing pitch attitude increases when the
CG is shifted forward, which also results in a significantly larger obscured segment. The obscured segment of the
14

Time
(
s
)
1
5
Pitch attitude (deg)
CG fore
CG middle
CG aft
Flying-V-1000
Airbus A350-1000
a) Pitch attitude angle
1
5
Time
(
s
)
Obscured segment (m)
CG fore
CG middle
CG aft
Flying-V-1000
Airbus A350-1000
b) Obscured segment
Fig. 13 Time histories comparison of pitch angle and obscured segment on the runway during landing, for different positions of the CG.
Flying-V-1000 can be up to twice as large as the one of the A350-1000, depending on the CG position.
C. Climb performance
Quasi-steady climb performance are calculated by trimming the aircraft at various points in the airspeed-altitude plane.
The aircraft is assumed to be in MTOM conditions, with the CG at its forward limit position. A throttle input of 85% is
imposed, to simulate the maximum continuous thrust available during climb and cruise operations [15, 36].
Figure 14 compares the maximum Angle of Climb (AoC) of both aircraft in the
ℎ
–
𝑉
flight envelope, and Figure 15
shows a similar comparison for the Rate of Climb (RoC). The solid black line highlights the locus of maximum values
of the respective flight parameters, hence providing the steepest and fastest climb trajectories, respectively. The drag
divergence Mach number 𝑀dd and the speed of sound are also drawn.
Both the AoC and RoC contours are comparable for the two aircraft. The Flying-V achieves its steepest climb
trajectory at a slightly lower airspeed than the A350, on average, while the two fastest climb trajectories are basically
0
0
0.5
0.5
1
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
100 150 200 250 300
True airspeed (m/s)
0
3
6
9
12
15
Altitude (km)
Max AoC (deg) Steepest
climb
a) Flying-V-1000
0
0
0.5
0.5
1
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
100 150 200 250 300
True airspeed (m/s)
0
3
6
9
12
15
Altitude (km)
Max AoC (deg)
Steepest
climb
b) Airbus A350-1000
Fig. 14 Maximum steady Angle of Climb (AoC) comparison in the ℎ–𝑉flight envelope, for maximum continuous thrust and MTOM.
15

0
0
0.5
0.5
2
2
4
4
6
6
8
8
10
12
14
100 150 200 250 300
0
3
6
9
12
15
Service ceiling
True airspeed (m/s)
Altitude (km)
Fastest
climb
Max RoC (m/s)
a) Flying-V-1000
0
0
0.5
0.5
2
2
4
4
6
6
8
10
12
14
100 150 200 250 300
True airspeed (m/s)
0
3
6
9
12
15
Altitude (km)
Service ceiling
Max RoC (m/s)
Fastest
climb
b) Airbus A350-1000
Fig. 15 Maximum steady Rate of Climb (RoC) comparison in the ℎ–𝑉flight envelope, for maximum continuous thrust and MTOM.
overlapping. Moreover, the Flying-V achieves a greater AoC and a higher RoC for every feasible combination of altitude
and speed. Since the two aircraft have the same
𝑇/𝑊
ratio, such performance advantage is due to its higher aerodynamic
efficiency [2].
These results also enable the Flying-V to achieve a higher service and absolute ceiling altitudes,
ℎserv
and
ℎabs
,
than the A350. The service ceiling has been calculated as the highest altitude where an aircraft can climb at a rate of
100
ft/min ≈
0
.
5 m
/
sat maximum continuous thrust, and is reported also in Figure 15. The absolute ceiling has been
computed as the highest altitude achievable at maximum available thrust (
𝛿𝑇=
1) with zero residual RoC. The service
and absolute ceiling altitudes are reported in Table 5.
Table 5 Service and absolute ceiling altitudes comparison at MTOM, forward-limit CG position.
Throttle setting Flying-V-1000 Airbus A350-1000
ℎserv 𝛿𝑇=0.85 12.0 km 10.6 km
ℎabs 𝛿𝑇=1.00 13.3 km 12.0 km
Lastly, Figure 16 shows the AoC achieved at speed
𝑉2
, with OEI, landing gear retracted, and maximum thrust
(
𝛿𝑇=
1) for both aircraft in take-off configuration. Certification specification CS25.121 dictates that a two-engined
aircraft should be able to achieve a steady AoC of 1
.
37
deg
in such conditions [
32
], and this limit is also reported in the
chart. The Flying-V achieves the required climb angle for all tested altitudes and mass fractions, while the A350 meets
the requirement for all but the most extreme case. Additionally, the Flying-V always achieves a larger AoC than the
A350, which decreases with increasing mass fraction and altitude.
D. Cruise performance
For the evaluation of cruise performance, each aircraft is trimmed at the nodes of a pre-defined grid in the
ℎ
–
𝑉
flight
envelope, in steady level flight and at MTOM. The relevant parameters are then extracted to calculate performance
metrics in trimmed flight conditions. With this approach, only instantaneous cruise performance is analyzed in the
present work.
The maximum values of the aerodynamic efficiency
𝐿/𝐷
, transonic efficiency
𝑀 𝐿/𝐷
, and Range Parameter
RP
are
compared for the two aircraft in Table 6, together with the corresponding Mach number and lift coefficient. Contour
plots of the RP as a function of the Mach number and the lift coefficient are shown in Figure 17.
The maximum trimmed
𝐿/𝐷
of the Flying-V-1000 is 17% higher than the one of the A350-1000. For both aircraft,
the maximum trimmed
𝐿/𝐷
is located at a smaller Mach number than the assumed cruise value of
𝑀=
0
.
85. This is
16

0.7 0.75 0.8 0.85 0.9 0.95 1
MTOM fraction
0
1
2
3
4
5
6
Angle of Climb with OEI (deg)
Required AoC in OEI conditions
h = 0 m
h = 1219 m
h = 2438 m
Flying-V-1000
Airbus A350-1000
Fig. 16 Climb angle comparison in steady One Engine Inoperative (OEI) conditions, 𝑉=𝑉2,𝛿𝑇=1, landing gear retracted.
most likely due to the implemented transonic wave drag model (Table 3b). The maximum transonic efficiency
𝑀 𝐿/𝐷
of the Flying-V-1000 is 21% higher than the one of the A350. Contrarily to the previous case, the maximum values
of the transonic efficiency occur at similar Mach numbers for both aircraft. When the least simplified metric is used,
these results are confirmed. The Flying-V-1000 achieves a maximum trimmed Range Parameter
RP
21% higher than its
competitor. When compared to the maximum
𝑀 𝐿/𝐷
, the maximum
RP
occurs in the same flight conditions for the
Flying-V, while it occurs at lower Mach number and higher
𝐶𝐿
for the A350. This is also suspected to be due to the
model used for the drag-divergence Mach number.
If both aircraft were to fly at the Mach number and lift coefficient that maximize
RP
with a mass equal to the MTOM,
this would yield a cruise altitude of 12
.
0
km
for the Flying-V and 11
.
3
km
for the A350. For the Flying-V, this is the
same altitude as its service ceiling. For the A350, such cruise altitude would be higher than its service ceiling, but lower
than its absolute ceiling at MTOM.
A more operational visualization of cruise performance is presented in the so-called “cruise grid” of Figure 18. This
chart shows that the cruise performance of the Flying-V remains vastly superior even when aircraft and fuel weight is
explicitly brought into the performance metrics. For the same mass fraction, the
SAR
of the Flying-V is significantly
greater than the one of the A350 at all Mach numbers relevant for cruise flight. Moreover, the
SAR
of the Flying-V at
MTOM is greater than the one of the A350 with mass fractions higher than 0.7 for
𝑀 >=
0
.
68. On the other hand, the
Flying-V achieves its maximum
SAR
at lower Mach numbers (on average) than the A350, for the same mass fraction.
Also, the cruise grid of the A350 appears to be flatter around the maximum than the one of the Flying-V, especially for
higher Mach numbers. This is important, as it allows the A350 to operate at cruise speeds higher than the optimal
one, while sacrificing only a small percentage of Specific Air Range. The
SAR
performance of the Flying-V seems to
decrease very rapidly as the Mach number increases towards the high transonic regime. This is surprising in light of
the very high drag-divergence Mach number predicted by the compressibility model used for this specific study, and
demands further investigation.
Table 6 Comparison of maximum cruise performance metrics in trimmed level flight at MTOM.
Perf. metric ΦFlying-V-1000 Airbus A350-1000
Φ𝑀|Φ𝐶𝐿|ΦΦ𝑀|Φ𝐶𝐿|Φ
(𝐿/𝐷)tr
max 23.7 0.75 0.37 20.3 0.65 0.71
(𝑀 𝐿/𝐷)tr
max 18.9 0.82 0.32 15.6 0.83 0.53
RPtr
max 9.7 0.82 0.32 8.0 0.75 0.69
17

0.3 0.4 0.5 0.6 0.7 0.8 0.9
Mach number
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Lift coefficient
4
4.5
4.5
5
5
5.5
5.5
6
6
6.5
6.5
7
7
7.5
8
8.5
9
9.5
Range Parameter
a) Flying-V-1000
0.3 0.4 0.5 0.6 0.7 0.8 0.9
Mach number
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Lift coefficient
4
4
4.5
4.5
5
5
5.5
5.5
6
6
6.5
7
7.5
8
Range Parameter
b) Airbus A350-1000
Fig. 17 Contour plots of the Range Parameter RP as a function of lift coefficient and flight Mach number, in trimmed level flight at MTOM.
0.6 0.65 0.70.75 0.80.85 0.9
80
100
120
140
160
180
200
220
MTOM
fraction
0.7
0.75
0.8
0.85
0.9
0.95
1
0.7
0.75
0.8
0.85
0.9
0.95
1
Mach number
Specific Air Range (m/kg)
Flying-V-1000
Airbus A350-1000
Fig. 18
Cruise grid comparing the Specific Air Range (
SAR
) of the Flying-V-1000 and the Airbus A350-1000 for different fractions of their respective
MTOM, in trimmed conditions at ℎ=11 km.
VI. Conclusions
This paper has presented an evaluation of the flight performance characteristics of the Flying-V-1000 and a comparison
to the ones of its envisioned competitor, the Airbus A350-1000. Identical thrust-to-weight ratios have been assumed for
both aircraft. Classic performance metrics related to the take-off, landing, climb and cruise mission phases have been
evaluated by means of a simple flight simulation framework.
On average, the Flying-V-1000 features a 25% shorter take-off distance and 30% shorter Balanced Field Length
(BFL) than the A350-1000. The first difference can mainly be attributed to the larger tail-strike pitch attitude of the
Flying-V, which results in significantly lower unstick and rotation speeds. The second difference is mainly due to the
superior breaking performance, due to a better relative placement of control surfaces and main landing gear.
Both aircraft have similar approach speeds and landing field lengths. Due to its highly swept wing, the Flying-V
18

approaches and touches down at a significantly larger pitch angle, leading to an increased de-rotation distance. On
the other hand, the Flying-V has a shorter ground run thant the A350 thanks to the nose-down attitude when on the
ground and to the aforementioned superior braking performance. Due to the large pitch angle at approach, the obscured
segment of the pilot’s vision during landing is considerably larger for the Flying-V than for the A350. This could
become problematic during operations, and requires further investigation.
Due to the higher maximum aerodynamic efficiency, the Flying-V outperforms the A350 in terms of climbing
performance. This is reflected in a higher service ceiling and absolute service ceiling, and slightly better compliance
with certification requirements for One Engine Inoperative (OEI) climb conditions.
The evaluation of the
SAR
has shown that the Flying-V-1000 outperforms the A350-1000 in terms of cruise efficiency
at basically all mass fractions and relevant Mach numbers. This result also stems from the 17% higher maximum
𝐿/𝐷
ratio for the Flying-V, as well as from its 10.8% higher drag divergence Mach number with respect to the A350.
It can be concluded that the Flying-V-1000 outperforms the A350-1000 model in terms of take-off, climb and cruise
performance for an identical thrust-to-weight ratio. The landing distances of the two aircraft are comparable, although
the significantly larger obscured segment of the pilot’s vision could cause problems for the Flying-V during landing with
poor visibility.
Further research could consider multi-body dynamics simulation for a precise analysis of the loads on the landing
gear during take-off and landing operations. In a similar way, locally or globally optimal mission simulation would
be advised to validate the instantaneous performance obtained for the climb and descent phases. Lastly, it would
be beneficial to increase the fidelity of the aerodynamic model, by means of using 3D panel methods and/or more
sophisticated models for compressibility and ground effect.
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