HIGHLY NON-PLANAR AIRCRAFT CONFIGURATIONS:
ESTIMATION OF FLIGHT MECHANICAL DERIVATIVES
USING LOW-ORDER METHODS
School of Engineering
Faculty of Aerospace Engineering
FH Aachen UAS
School of Engineering
Faculty of Aerospace Engineering
FH Aachen UAS
Highly non-planar aircraft configurations promise vast improvements concerning aircraft efficiency, but their
flight mechanical properties are currently not well understood. Using reference wind tunnel data and RANS
CFD (STAR-CCM+) results, a vortex lattice solver (VSPAERO) and a surface vorticity flow solver
(FlightStream) are being evaluated concerning their ability to model joined and box wing longitudinal aerody-
namic characteristics. It is shown that FlightStream is able to provide results of CFD-like quality, as long as
flow separation effects do not become prominent. VSPAERO delivers good lift and pitching moment results,
but lacks in drag modelling. STAR-CCM+’s solutions come very close to wind tunnel results.
AoA = angle of attack
b = wing span
CFD = computational fluid dynamics
= mean aerodynamic chord length
= pitching moment derivative w.r.t. AoA
LE = leading edge
= length of geometry
q = dynamic pressure
RANS = Reynolds-averaged Navier–Stokes
Re = Reynolds number
T = temperature
t/c = airfoil thickness to chord ratio
V = free stream velocity
VLM = vortex lattice method
ρ = density
λ = wing taper ratio
EU’s Flightpath 2050 studies estimate a growth of global
air traffic from 2.5 billion passengers in 2011 up to 16 billion
passengers in 2050. Especially in the face of climate
change, Flightpath 2050 aims high for reducing air traffic
related emissions. Ambitious goals of 75% less CO2 and
90% less NOx emissions per passenger and kilometer, as
well as noise reduction of 65% require significant improve-
ments in efficiency.
These improvements can only be achieved employing rad-
ically new concepts in the near term, rather than focusing
on evolutionary development of aircraft design and opera-
tion. A profound understanding of more efficient configura-
tions without extensive and time-consuming flight test cam-
paigns warrants timely development of these enhanced
technologies. Refining aerodynamic efficiency through un-
conventional wing configurations appears to be a promising
aid in achieving significantly less emissions. Conducting vir-
tual flight tests supported by accurate aerodynamic anal-
yses helps reducing time to service of new concepts. Such
configurations for reduced drag  or structural weight are
the box or joined wing  concepts, where two longitudinally
and vertically staggered lifting surfaces are joined at their
tips (box wing) or along the span (joined wing).
Highly non-planar configurations can be applied to a wide
variety of aircraft designs, ranging from agricultural air-
planes  and commercial transports  to exotic VTOL ap-
plications . Complete flight mechanical behavior of these
aircraft is not as well researched by the scientific commu-
nity, as the conventional aircraft configuration. In order to
enable application of this wing concept to new aircraft de-
signs, a thorough investigation of flight mechanical cou-
plings, flight dynamics and specific design parameters such
as horizontal and vertical wing spacing is required. In order
to size aircrafts taking advantage of unconventional config-
urations all these new considerations need to be combined
into an multidisciplinary design optimization (MDO) tool [5,
6]. Even with today’s computing power, extensive parame-
ter studies are feasible only using low-order surface meth-
ods rather than time-consuming CFD calculations that solve
a fluid volume. In these authors’ literature review no exam-
ples of validation of current monoplane approximation
methods applied to the unique design of the box-wing air-
craft have been found.
Using three different validation cases, a vortex lattice imple-
mentation (VSPAERO) and a surface vorticity solver
(FlightStream) are evaluated concerning their ability to
model longitudinal motion aerodynamics of highly non-pla-
nar aircraft configurations. These results are compared
against RANS CFD results (using Siemens’ StarCCM+)
and wind tunnel data.
This paper is structured in the following way: Subsequent
to this introduction section 2 covers the validation cases
used. Thereafter section 3 briefly introduces the tools used
to perform this study. Then the results of the aerodynamic
analyses are presented and discussed in section 4. Finally
conclusions are drawn to which extend the flight envelope
can be modeled using data from these low-order sources
and whether an extension of the envelope can be achieved
by modifying the low-order methods (section 5).
2. OVERVIEW OF THE VALIDATION CASES
The current literature features many box wing aerodynamic
studies using simulation, analytical and parametric meth-
ods [7–10]. Research has shed light on the aerodynamic
benefits of the box-wing design. Although much data exists,
literature shows very few experimental analyses of box
wing configurations. Published data often does not give the
required geometry information to allow a reproduction of re-
sults using numerical methods .
In order to quantify the applicability of different aerodynamic
calculation methods for flight model generation, a three-
step approach was chosen: Three configurations of in-
creasing complexity have been analyzed, two of them
backed up by available wind tunnel data. Each configura-
tion has been built using the parametric geometry modeler
OpenVSP  from which they are being exported into dif-
ferent file formats required by the aerodynamic calculation
This study attempts to fill the gap between a simple wing
system with neither taper, twist nor sweep on the one hand
 (section 2.1) and a realistic full aircraft model including
fuselage, empennage and nacelles  (section 2.3) with a
generic design of intermediate complexity (section 2.2). The
public domain contains sufficient data to allow digital recon-
struction of the wind tunnel experiments of both extremes
of the spectrum. There is no wind tunnel data of the generic
design available so it only serves as a comparison of the
different numerical methods applied.
In the subsequent paragraphs each validation case is de-
scribed in detail. The procedure and reasoning behind ge-
ometry generation and flow condition selection is re-
2.1. NASA biplane-winglet configuration
The most basic configuration analyzed in this study has
been tested by Gall  in Pennsylvania University’s wind
tunnel in 1984. The mentioned publication validates vortex
lattice code with a reflection plane wind tunnel model of a
box wing system, called a biplane-winglet configuration by
the author (Figure 1).
It consists of two main wings with NACA 0012 airfoil, set
apart by a stagger of 1 chord length and a gap of 1 chord
The endplates are made up from wooden sheets, hand
sanded to form a 3% thick symmetrical airfoil, bolted to the
side of both wings.
Figure 1: OpenVSP model of a biplane-winglet configura-
tion according to 
2.1.1. Model buildup
Both wings have been modelled as NACA 0012 airfoils, air-
foil coordinates automatically generated by OpenVSP.
The first approach to modelling of the endplates used a ge-
neric NACA 0003 airfoil. This solution poses problems for
CFD modelling due to its very sharp trailing edge. The au-
thors instead elected to generate a custom airfoil that better
resembles a rounded flat plate.
Geometry parameters are summarized in Table 1.
Table 1: Biplane-winglet configuration parameters
b 1 m
wing airfoil NACA 0012
endplate airfoil rounded flat plate
symmetrical, 3% thick-
2.1.2. Flow conditions
Gall  provides wind tunnel test velocity, temperature, as
well as barometric pressure. Tests were conducted at a
chord Reynolds number of approximately 510,000.
Table 2: Biplane-winglet configuration flow conditions
V 45.42 m/s
p 98239.13 Pa
T 319.26 K
ρ 1.072 kg/m
2.2. Generic box wing system
In order to bridge the gap between the vastly different com-
plexities of the other two models a generic box wing system
has been designed (Figure 2).
Figure 2: Generic box wing configuration in OpenVSP
2.2.1. Model buildup
This configuration employs NACA 6-series laminar flow air-
foils, wing sweep as well as taper. Corners have been
rounded to match conventional box wing configurations.
The rear wing is mounted at an incidence of -1° to achieve
positive static stability. The wing tapers from a root chord of
1 m to 0.5 m at the tip and vertical joint. The front and rear
portion of the wing both feature positively cambered airfoils.
The vertical part is composed of a symmetrical airfoil. The
front wing’s airfoil has a design lift coefficient of 0.5, the rear
wing’s airfoil 0.2.
Table 3: Generic box wing geometric reference data
b 9.3 m
moment reference 1.75 m aft of front root LE
2.2.2. Flow conditions
Flow conditions have been selected to be insensitive to
Reynolds number, as well as compressibility effects.
Table 4: Generic box wing flow conditions
V 50 m/s
p 98239.13 Pa
T 319.26 K
2.3. NASA JW-1 configuration
The most complex validation model is that of NASA’s JW-1
research aircraft concept (Figure 3).
At the end of the 1980s NASA, in collaboration with ACA
Industries, designed a research aircraft that employs a
joined wing configuration . The joined wing concept con-
sists of two wings, the primary wing providing most of the
lift, the secondary wing acting as a strut for main wing bend-
ing moment relief. In addition to relieving bending moment
and thus reducing structural weight, the second wing can
also be designed to reduce induced drag according to
Prandtl’s biplane theory .
Figure 3: NASA JW-1 OpenVSP model
The cited wind tunnel experiments have been conducted in
the NASA Ames 12-ft wind tunnel. The aim of the investiga-
tion was to assess performance, stability and control char-
acteristics of the design in preparation of building the air-
craft and full scale flight testing . Because of the serious
nature and scale of the tests, it can be assumed that the
data available has been carefully calibrated for known wind
tunnel specific errors.
2.3.1. Model buildup
Smith and Stonum  give detailed geometry information
on the aircraft. While the fuselage geometry presented dif-
fers between publications ( vs. ), it is stated that the
full scale aircraft would re-use the existing AD-1 fuselage
and engines. According to  the existing AD-1 fuselage
wind tunnel model has also been re-used for the cited ex-
periments. No data on any modification made from AD-1
wind tunnel fuselage design to full scale aircraft production
has been found. This is why the fuselage layout used for
this simulation has been carefully modelled after AD-1
drawings, the latter being available in higher quality .
Flow-through nacelles are used in place of engines in the
wind tunnel model. No information has been found on na-
celle wall thickness or profile. A modified NACA 4-series
airfoil with a t/c of 1.5% has been employed. The wing con-
figuration has solely been modelled after available JW-1 3-
views and numerical data given in . The specified rear
wing sweep angle of -32.0° did not allow matching given 3-
views. This has been changed to inversely match the front
wings’ sweep at -30.5°. Presented airfoil coordinates
needed conversion to a format suitable for OpenVSP and
corrected for sweep angle. While airfoils are defined per-
pendicular to the quarter chord line, OpenVSP only accepts
airfoil sections parallel to the body fixed x-coordinate. Not
accounting for sweep would result in too high a t/c value.
2.3.2. Flow conditions
Smith et.al. quote a chord Reynolds number of approxi-
mately Re = 10
 for their experiments. The cited paper
contains analyses of three different configurations with
slightly different mean aerodynamic chord lengths. Flow
conditions have been numerically optimized to match a
chord Reynolds number of 10
for the given JW-1 C
0.1486 m, while also matching Mach number and dynamic
pressure as given in Table 5.
Table 5: JW-1 wind tunnel flow conditions
q 8140 Pa
ρ 1.0443 kg/m
V 124.86 m/s
T 316.61 K
3. GEOMETRY GENERATION AND SIMULATION
The following section provides a brief overview of the tools
used for conducting the validation. For each tool a short de-
scription of the workflow applied is given.
Filling NASA’s need for an easy to use parameterized ge-
ometry modeler, initially the Rapid Airplane Modeler (RAM)
has been developed. It has later evolved into Vehicle
Sketch Pad (VSP), a tool that allows aircraft geometry gen-
eration using a multitude of shapes, defined by engineering
parameters. The GUI tool does not only serve geometry
generation, but also provides conceptual design analysis
methods, as well as exports into different file formats for
further processing . The software has been released to
the public as an open source project in 2012, thereby be-
The parametric approach allows precise reverse-engineer-
ing of geometries from drawings with limited effort. In this
study three-view drawings are used in conjunction with
given numerical geometry information to recreate wind tun-
3.2. VSPAERO (VLM)
The least precise but fastest aerodynamic analysis method
used in this publication is VSPAERO. It is a linear vortex
lattice solver developed by David Kinney of NASA Ames
Research Center . The tool allows integrated control
surface deflection analyses by tilting surface normals of the
VLM geometry. Aero-propulsive effects can also be mod-
elled using actuator disks. An OpenVSP model can be fed
directly into the vortex lattice toolchain without any need for
manual mesh generation. Tessellation information is de-
ducted from the geometric parameters of the model. In ad-
dition to linear VLM theory, VSPAERO uses a very simple
parasite drag estimation procedure. Friction drag of individ-
ual components is approximated using a friction drag cor-
relation by Schlichting , then multiplied by fixed percent-
ages to account for form and interference drag.
Between linear vortex lattice theory and STAR-CCM+’s vol-
ume based RANS CFD approach lies FlightStream’s sur-
face vorticity flow methodology.
FlightStream provides a surface vorticity flow solver for sub-
and transonic analyses. The quality of its solutions is driven
by automatic post-processing of the linear surface vorticity
solution. This post-processing enables simulation of bound-
ary layer transition, as well as separation effects.
Initial meshing is provided by OpenVSP through geometry
tessellation specifications. OpenVSP’s CompGeom tool is
used for intersecting all geometric components and gener-
ating a single watertight, triangulated surface mesh. This is
then exported, either as an *.stl or *.plot3d file to
FlightStream. Inside FlightStream trailing edges and wake
termination nodes need to be marked, this happens through
a highly automatized process. When initializing the solver
mesh, FlightStream then tries to convert the triangular
mesh elements into flow-parallel quadrilateral elements in
order to increase solver performance.
Simcenter STAR-CCM+ is a commercial multiphysics com-
puter aided engineering software suite that includes numer-
ical methods for solving a variety of engineering problems,
ranging from stress analysis to flow simulations including
chemical reactions. It has been validated for a variety of test
cases , including many aerospace applications and is a
popular tool in industry.
For the analyses presented herein it is used for computa-
tional fluid dynamics (CFD) using Reynolds-averaged Na-
vier–Stokes (RANS) equations. Due to the low Mach num-
bers of all experiments, incompressible flow is assumed
and the Semi Implicit Method for Pressure Linked Equa-
tions (SIMPLE) is applied. This leads to a significant reduc-
tion of computational cost. In order to simulate the effects
of a turbulent boundary layer, a k-ω turbulence model is
used. Here its results are primarily used to validate correct
geometry reproduction from available reference data.
OpenVSP exports the model component-wise as high res-
olution *.stl geometry files that are then imported into
STAR-CCM+. In order to create the computational domain,
the parts to be analyzed are subtracted from a sufficiently
large bullet shaped flow field (length = 100 x L
= 50 x L
). Finite volume discretization is conducted us-
ing STAR-CCM+’s unstructured Cartesian cut cell mesher
with a dedicated prism layer for boundary layer simulation.
Boundary layer mesh parameters have been chosen to
yield a y+ = 1 at the surface and capture the whole bound-
ary layer thickness with the prism mesh.
Grid independence studies lead to mesh sizes of 13 to 30
million cells, depending on the geometry’s complexity.
4. COMPARISON OF AERODYNAMIC DATA
This section shows the results obtained using the three dif-
ferent numerical methods. Differences in accuracy are dis-
cussed and possible root causes are analyzed.
4.1. NASA biplane-winglet configuration
Gall  provides lift and drag coefficient data only.
Coefficients are given with an accuracy of 3 decimal places
for 12 different angles of attack between -2° and 21° AoA.
The author accounts for a variety of wind tunnel induced
errors, as documented in .
Error bars scaled to 5% of the respective values at 10 to
12° AoA have been added to the wind tunnel data in all fig-
The comparative study started with the investigation of pos-
sible differences in lift simulation.
Figure 4 shows biplane-winglet total lift coefficient with re-
spect to angle of attack. Both FlightStream and STAR-
CCM+ approximate linear lift curve slope with high preci-
sion. VLM estimates a lower lift curve slope. In comparison
to simulations without winglets, VLM fails to capture any ef-
fect of the perpendicular winglet on lift curve slope. Gall 
has conducted experiments without winglet as well and was
able to demonstrate a positive effect of the winglet on lift
curve slope. This effect is less prominent in the joined wing
simulations (section 4.3.1) as dihedral is limited to a less
extreme -20°. A decreased lift curve slope in the wind tun-
nel data between -2° and 2° AoA can possibly be attributed
to experimental error as it is not captured by any of the nu-
Figure 4: NASA biplane-winglet lift curve, error bars show
Figure 5 shows the biplane-winglet drag curve.
FlightStream and STAR-CCM+ show accurate drag predic-
tion up to an angle of attack of 6°. VSPAERO underesti-
mates wing efficiency, again not capturing the increased ef-
ficiency due to the winglet. Zero lift drag estimation of
VSPAERO on the other hand provides credible results. In
contrast to the JW-1 configuration (section 4.3.2), drag is
underestimated by all numerical methods. As the wind tun-
nel model does not appear to be of a high quality (“the wing-
winglet joint was filleted with putty during experimental
tests” , winglet has been bolted to the side), increased
parasite drag compared to the clean numerical calculations
can be assumed.
Figure 5: NASA biplane-winglet drag curve, error bars
show ±45 drag counts
4.2. Generic box wing configuration
Compared to NASA’s biplane-winglet configuration this
wing geometry poses additional challenges for the compu-
tational methods at hand. Symmetric wing sweep of both
wings leads to changing absolute stagger (5.7 m to 3.6 m)
and thereby variations in interference along the span-wise
direction of the wing. Moderate front wing dihedral also
leads to changes in gap between both wings.
Both comparisons of wind tunnel data to STAR-CCM+ in
this paper support the validity of the CFD simulation ap-
proach taken throughout the publication, so STAR-CCM+ is
used as the reference for this configuration.
All graphs contain error bars scaled to 5% of the respective
STAR-CCM+ data at 12° AoA.
Calculated lift curves are shown in Figure 6.
STAR-CCM+ data suggests a gradually decreasing lift
curve slope with increasing AoA. A linear lift curve can be
assumed up to about 4° AoA. Lift curve slope is overesti-
mated by both VSPAERO and FlightStream. The previous
experiment demonstrated that VSPAERO is not able to pre-
dict vertical winglet contribution to lift curve slope, so the
vertical part of the box wing does most probably not con-
tribute to this effect. Wing sweep is more prominently pre-
sent in the JW-1 configuration analyzed in section 4.3 and
lift curve slope is accurately estimated by both FlightStream
and VSPAERO in this configuration. The high degree of
stagger and gap between the wings is the striking difference
-4 -2 0 2 4 6 8 10 12
wind tunnel FlightStream
-4 -2 0 2 4 6 8 10 12
wind tunnel FlightStream
between the other two configurations and this one. This
leads to the conclusion that both lower order methods em-
ployed here underestimate the downwash effect in high
stagger / gap scenarios. FlightStream’s flow separation es-
timation triggers at an angle of attack similar to STAR-
CCM+, but does not show the distinct flattening of the lift
curve slope that RANS CFD predicts. The decrease in lift
curve slope in STAR-CCM+’s solution seems to be caused
by flow separation effects that FlightStream is not able to
Figure 6: Generic box wing configuration lift curve,
error bars show ±0.07 C
Figure 7 shows the generic box wing configuration’s total
drag coefficient with respect to angle of attack.
FlightStream matches STAR-CCM+’s drag prediction up to
higher angles of attack. VSPAERO highly overestimates
wing efficiency, and underpredicts zero lift drag by a factor
of two. Figure 8 shows the drag polar, including aforemen-
tioned error bars for lift and drag coefficients. Between
= 0.45 and C
= 0.91 FlightStream’s drag prediction lies
within ±10 drag counts of the STAR-CCM+ results. Below
this range it predicts higher drag, above this range pre-
dicted drag is lower. This stems from an overestimation of
minimum drag and minimum drag lift coefficient, as well as
a slight overestimation of wing efficiency.
Figure 7: Generic box wing configuration drag curve, error
bars show ±45 drag counts
Figure 8: Generic box wing configuration drag polar, error
bars according to previous graphs
4.2.3. Pitching moment
Pitching moment coefficient with respect to angle of attack
is shown in Figure 9.
FlightStream matches STAR-CCM+’s pitch stability deriva-
tive from -3° to 6° AoA, but overestimates zero lift pitching
moment by 7%. As lift curve slope decreases, pitch stability
increases and CFD results start to deviate from
FlightStream above 6° AoA. VSPAERO underpredicts zero
lift pitching moment by 14% and also underpredicts pitch
-4 -2 0 2 4 6 8 10 12 14 16 18
FlightStream STAR-CCM+ VSPAERO
-4 -2 0 2 4 6 8 10 12 14
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Figure 9: Generic box wing configuration pitching moment
curve, error bars show ±0.05 C
4.3. NASA JW-1 configuration
The JW-1 joined wing wind tunnel model was the most com-
plex geometry analyzed, but the available data quality was
also the highest. This explains why STAR-CCM+ data is ac-
tually very close to NASA’s wind tunnel experiments, while
FlightStream does not match STAR-CCM+ as close as it
does for the biplane-winglet configuration. Existing wind
tunnel data given in the form of graphs in  has been dig-
itized to ease visualization. It has to be noted that
VSPAERO was unable to simulate fuselage and engine na-
celles. The solutions contained inexplicable errors with
these geometries included.
The graphs show error bars added to the wind tunnel data.
They are scaled to 5% of the respective values at 4° AoA.
Figure 10 shows total lift coefficient with respect to angle of
attack of the NASA JW-1 wind tunnel model.
All methods approximate linear lift curve slope with only mi-
nor deviations, as expected. VLM and FlightStream pro-
duce linear lift curve slopes, while STAR-CCM+ is able to
capture a slight decrease in lift curve slope above 2° AoA.
Original wind tunnel result analyses indicated an onset of
separation effects above 2° AoA . As these separation
effects can hardly be modeled by vorticity based solutions,
FlightStream and VSPAERO do not show their conse-
quences. The general underestimation of lift by the numer-
ical methods might origin in imprecise referencing of the ge-
ometry’s zero-lift line, as there is no reference in the geo-
metrical data available. Component-wise analysis shows
that FlightStream’s underestimation of total lift relative to
the STAR-CCM+ solution stems from an underestimation of
rear wing lift. This could be due to an overestimation of in-
duced downwash effect downstream of the front wing.
Figure 10: NASA JW-1 lift curve, error bars show ±0.05 C
Figure 11 shows total drag coefficient with respect to angle
of attack of the NASA JW-1 wind tunnel model.
FlightStream, as well as STAR-CCM+ overestimate drag up
to 4° AoA. As the through flow nacelle geometry has been
created using engineering judgement alone, it is valid to as-
sume part of the cause for this overestimation here.
Figure 11: NASA JW-1 drag curve,
error bars show ±30 drag counts
-4 -2 0 2 4 6 8 10 12 14
-8 -6 -4 -2 0 2 4 6 8
wind tunnel FlightStream
-8 -6 -4 -2 0 2 4 6 8
wind tunnel FlightStream
The drag rise due to significant flow separation effects past
4° AoA is no longer captured by both numerical methods.
The minimum drag AoA range between -5° and -2.5° is cap-
tured within 30 drag counts by STAR-CCM+. FlightStream
seems to overestimate minimum drag with respect to both
STAR-CCM+ and wind tunnel data. As expected linear VLM
underpredicts minimum drag by the significant amount of
. Skin friction and pressure drag effects are not
modelled by basic linear VLM theory, so VSPAERO esti-
mates zero lift drag using very basic methods.
The fact that VLM does not capture the drag increase below
-5° AoA can be attributed to the missing fuselage and en-
gine geometries. Fuselage only wind tunnel testing by
Smith and Stonum  indicates approximately symmet-
rical drag characteristics about circa -1° to 0° AoA. As the
wings are mounted to the fuselage at a very high angle of
incidence (7.5° at the front wing root), their minimum drag
AoA is far below the fuselage minimum drag angle.
This mismatch between minimum drag angles cannot be
traced back to careless aerodynamic design of the aircraft
but is owed to the projects use of the existing AD-1 fuse-
lage. With its short landing gear the JW-1 needed to provide
at low pitch angles to avoid tail strike .
4.3.3. Pitching moment
Figure 12 pitching moment coefficient with respect to angle
STAR-CCM+ results match experimental data closely. The
region of linear C
between -5° and 2° AoA, as well as de-
creased stability below -5° and above 2° is also simulated.
The decrease in C
at positive angles of attack caused by
flow separation effects is underestimated. FlightStream is
able to track C
up to 2° AoA as well, losing fidelity when
flow separation effects start to dominate. As outlined in sec-
tion 4.3.1 already, rear wing lift is underestimated, leading
to a too low total C
estimation. This also explains the over-
estimation of C
, as lift acting on the rear wing has a neg-
ative influence on pitching moment. VLM overestimates sta-
bility, because the fuselage’s destabilizing contribution is
not represented by the geometry.
In order to judge how well the numerical methods predict
the trim condition Figure 13 shows pitching moment with
respect to lift coefficient. Error bars have the same size as
in previous graphs. It can be seen that FlightStream and
STAR-CCM+ estimate on either side of the experimental
results. The C
curve slope is estimated best by STAR-
CCM+. FlightStream again overestimates its steepness at
increasing angles of attack.
Figure 12: NASA JW-1 pitching moment curve,
error bars ±0.01 C
Figure 13: NASA JW-1 pitching moment / lift curve, error
bars according to previous graphs
-8 -6 -4 -2 0 2 4 6 8
wind tunnel FlightStream
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
wind tunnel FlightStream
5. APPLICATION FOR FLIGHT MODELLING
When generating an aerodynamic database for flight dy-
namics modelling purposes, applicability of the methods
employed must be carefully assessed. This study can only
provide guidance with respect to longitudinal motion simu-
lation, as the effect of side slip on the methods’ accuracy
has not been analyzed.
It has been shown that VSPAERO is useful for quick as-
sessment of lift and pitching moment characteristics of a
highly non-planar aircraft configuration. It has to be kept in
mind that it does not seem to properly take into account
vertical surfaces – applicability is thereby limited to joined
wing systems, which do not feature vertical struts that have
significant influence on wing aerodynamics. Induced drag
estimates of the joined wing configuration seem appropri-
ate, box wings joined by vertical struts do not yield satisfac-
tory results. Parasite drag estimation fails with the introduc-
tion of laminar flow airfoils or program errors that exclude
parts of the geometry from being included in the simulation.
OpenVSP contains a submodule for detailed parasite drag
analysis using a variety of drag buildup methods. Pre-
liminary experiments show promising results when merging
VSPAERO’s induced drag with zero lift drag obtained from
the specialized submodule.
FlightStream has proven to be very useful for lift, drag and
pitching moment derivative estimation in conditions without
prominent flow separation effects. It can handle vertically
joined struts much better than VSPAERO. FlightStream as
well as VSPAERO have trouble estimating lift curve slope
of high stagger / gap scenarios. Given the computational
speed advantages over STAR-CCM+, it is a useful tool for
geometric parameter studies.
The RANS CFD calculations using STAR-CCM+ match
wind tunnel data very well, even when flow separation starts
to develop. Stall behavior still proves to be hard to model. If
computational power is not a limiting factor, RANS CFD
proves to be the method of choice for accurate aerody-
Investigations concerning flight mechanics of highly non-
planar aircraft configurations make adequate simulation
models necessary. In this paper it has been shown that ac-
ceptable aerodynamic models can be generated without ex-
cessive computational power using low order methods.
This publication specifically attempts to validate VSPAERO
and FlightStream against STAR-CCM+ and all three nu-
merical methods against wind tunnel data. It has been
demonstrated that contemporary low order methods allow
accurate predictions of aerodynamic characteristics, includ-
ing drag, at moderate angles of attack. A guideline has
been presented as to which geometric features impede
method accuracy. It still needs to be verified whether the
above mentioned conclusions can also be applied to lateral
For a limited resources project, or if many different configu-
rations need to be analyzed, FlightStream proves to be the
method of choice. Individual results can then be backed up
by RANS CFD calculations, if desired. For large parameter
studies concerning lift, pitching moment and induced drag
only, VSPAERO can be efficiently employed to speed up
The authors like to express their gratitude to Siemens PLM
Software for providing academic licenses of their software
 European Commission, Flightpath 2050: Europe's vi-
sion for aviation; maintaining global leadership and
serving society's needs; report of the High-Level
Group on Aviation Research. Luxembourg: Publ. Off.
of the Europ. Union, 2012.
 I. Kroo, “Nonplanar Wing Concepts for Increased Air-
craft Efficiency,” Jun. 10 2005.
 J. Wolkovitch, “The joined wing - An overview,” Jour-
nal of Aircraft, vol. 23, no. 3, pp. 161–178, 1986.
 D.F. Finger, C. Braun, and C. Bil, “A Review of Con-
figuration Design for Distributed Propulsion Transi-
tioning VTOL Aircraft,” Asia-Pacific International
Symposium on Aerospace Technology APISAT
 J. Schirra and J. Watmuff, “Euler-based induced
drag estimation for highly non-planar lifting systems
during conceptual design,” Deutscher Luft- und
Raumfahrtkongress 2013, Stuttgart, Germany, Sep.
2013. [Online] Available: https://www.re-
 Alexander Spohr, J. Schirra, Joschka Hoefling, and
Andreas Schedl, “Wing Weight estimation methodol-
ogy for highly non-planar lifting systems during con-
 Fabio Cruz Riberio, Adson Agrico de Paula, Dieter
Scholz, and Roberto Gil Annes da Silva, “Wing geo-
metric parameter studies of a box wing aircraft con-
figuration for subsonic flight,” (Eng), 7th European
Conference for Aeronautics and Space Sciences
 T. Chau and D. W. Zingg, “Aerodynamic Shape Opti-
mization of a Box-Wing Regional Aircraft Based on
the Reynolds-Averaged Navier-Stokes Equations,” in
35th AIAA Applied Aerodynamics Conference, Den-
ver, Colorado, 06052017, p. 182.
 P. O. Jemitola, “Conceptual design and optimization
methodology for box wing aircraft,” PhD Thesis,
Cranfield University, Cranfield, 2012.
 J. Schirra, W. Bissonnette, and G. Bramesfeld,
“Wake-Model Effects on Induced Drag Prediction of
Staggered Boxwings,” Aerospace, vol. 5, no. 1, p.
 C. Galinski et al., “Wind tunnel tests of the inverted
joined wing and a comparison with CFD results,” Air-
craft Eng & Aerospace Tech, vol. 47, no. 9, p. 0,
 A. Hahn, “Vehicle Sketch Pad: A Parametric Geome-
try Modeler for Conceptual Aircraft Design,” in 48th
AIAA Aerospace Sciences Meeting including the
New Horizons Forum and Aerospace Exposition, Or-
lando, Florida, 2010.
 P. D. Gall, “An experimental and theoretical analysis
of the aerodynamic characteristics of a biplane-wing-
let configuration,” NASA-TM-85815, Jun. 1984.
 S. C. Smith and R. K. Stonum, “Experimental Aero-
dynamic Characteristics of a Joined-wing Research
Aircraft Configuration,” NASA, NASA Ames Re-
search Center, Moffett Field, CA, United States
NASA-TM-101083, A-89074, NAS 1.15:101083, Apr.
1989. [Online] Available:
Accessed on: Sep. 06 2019.
 S. Smith, S. Cliff, and I. Kroo, “The design of a joined
wing flight demonstrator aircraft,” in Aircraft Design,
Systems and Operations Meeting, Saint Louis, MO,
USA, 09131987, p. 7711.
 E. V. Laitone, “Prandtl's biplane theory applied to ca-
nard and tandem aircraft,” Journal of Aircraft, vol. 17,
no. 4, pp. 233–237, 1980.
 NASA Dryden Flight Research Center, AD-1 3-view.
[Online] Available: https://www.dfrc.nasa.gov/Gal-
on: Sep. 20 2019.
 J. A. Garcia, J. V. Bowles, D. J. Kinney, J. E. Melton,
and X. J. Jiang, “VIPER Integrated MDAO Analysis
for Conceptual Design of Supersonic X-Plane Vehi-
cles,” NASA, NASA Ames Research Center
NASA/TM—2019–220239, Jul. 2019. [Online] Avail-
Accessed on: Sep. 21 2019.
 H. Schlichting and K. Gersten, Boundary-Layer the-
ory. Berlin, Heidelberg: Springer Berlin Heidelberg,
 CD-adapco, Validation of Star-CCM+ for External
Aerodynamics in the Aerospace Industry. [Online]
adapco_AeroValidation_v7.pdf. Accessed on: Sep.
 OpenVSP Parasite Drag Tool. [Online] Available:
Accessed on: Sep. 24 2019.