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Effects of Taper Ratio on Aircraft Wing Aerodynamic Parameters: A Comperative Study

  • 21.49
  • University of Turkish Aeronautical Association
  • 1.57
  • Iskenderun Technical University

Abstract and Figures

Wing design is one of the most important tasks for a designer to overcome during an aircraft design process. Therefore, a designer need to optimize so many wing geometrical parameters with the aim of obtaining an efficient wing geometry complying with requirements of the design. Taper ratio is one of these parameters, which is the ratio of root and tip chord lengths of a wing. In this study, firstly, a high aspect ratio rectangular aircraft wing was numerically investigated in terms of some aerodynamic parameters including induced drag coefficient, Oswald efficiency factor and lift coefficient together with its span-wise distribution by means of XFLR5 computational fluid dynamics program. The assessment of mesh accuracy of the program was done at the beginning of the analyses. Later on, with the aim of observing the effects of taper ratio on aircraft wing aerodynamic parameters, the revised versions of the wing, which have the taper ratios from 0.2 to 1.2 (with the increment of 0.2) were analyzed. In conclusion, depending on the analyses results, the wings having different taper ratios were compared in terms of obtained aerodynamic parameters and span-wise lift distributions. Moreover, tip vortices of each wing, together with their sizes, were obtained and also compared.
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Conference Paper
3rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
Çukurova University, Congress Center, October 24-26, 2018, Adana / TURKEY
Pages: 1-6, Paper ID:152
An arcraft desgner has so many tasks to overcome durng
an arcraft desgn process. One of the most mportant tasks
s to desgn an ecent wng complyng wth the determned
requrements. s s generally possble wth optmzng so
many geometrcal and aerodynamc parameters of the wng
Geometrcally, arfol and planform geometres are the man
terms to defne a wng. An aerodynamcally ecent wng
can be desgned when the sutable arfol(s) and planform
geometry coupled. erefore, planform geometry s one of
the most mportant geometres durng an arcraft desgn
process. Taper rato s one of the parameters on planform
geometry whch means the rato of the root and tp chord
lengths of a wng. Hence, ts eects on wng’s aerodynamc
parameters are also mportant and should be taken nto con-
sderaton durng a wng desgn process [2] [3].
e eects of the taper rato on wng aerodynamc parame-
ters can be obtaned by means of numercal or expermental
analyses [4]. At the conceptual desgn phase of an arcraft,
t can be preferable to use computatonal ud dynamcs
programs rather than tme consumng expermental setups.
ere are so many programs to perform these analyses such
as Ansys Fluent, XFLR5 and Soldworks Flow Smulaton.
In the lterature, ncludng numercal analyses, there are so
many studes about nvestgatng the aerodynamc parame-
ters of arcraft wngs.
Della Veccha et al. [5] nvestgated eects of propellers on
wng aerodynamcs by means of a computatonal ud dy-
namcs program. e study ncludes eects of propellers
mounted at both tp and mddle of the wng. Frstly, mesh
accuracy of the program was done and t was shown that the
program results are n good agreement wth expermental
results. Later on, by means of usng the valdated method
on numercal analyses, they obtaned that the tp-mounted
propeller can decrease the nduced drag from up to 10% and
mddle-mounted propellers can ncrease the maxmum lft
coecent of the wng up to 30%. Bravo-Mosquera et al.
[6] presented conceptual desgn and prototype of an agr-
cultural arcraft. Followng the tradtonal desgn methods
appled, sx derent wnglet desgns, whch have derent
cant angles were analyzed by means of a computatonal ud
dynamcs program usng Reynolds–Averaged–Naver–Sto-
Eects of Taper Ratio on Aircraft Wing Aerodynamic Parameters:
A Comperative Study
İbrahim Halil Güzelbey1, Yüksel Eraslan2*, Mehmet Hanifi Doğru3
1Aircraft and Aerospace Engineering Department/Gaziantep University, Turkey;
2Aircraft and Aerospace Engineering Department/Gaziantep University, Turkey;
3Pilotage Department/Gaziantep University, Turkey;
Wing design is one of the most important tasks for a designer to overcome during an aircraft design process.
erefore, a designer need to optimize so many wing geometrical parameters with the aim of obtaining an
ecient wing geometry complying with requirements of the design. Taper ratio is one of these parameters,
which is the ratio of root and tip chord lengths of a wing. In this study, rstly, a high aspect ratio rectangular
aircraft wing was numerically investigated in terms of some aerodynamic parameters including induced drag
coecient, Oswald eciency factor and lift coecient together with its span-wise distribution by means of
XFLR5 computational uid dynamics program. e assessment of mesh accuracy of the program was done
at the beginning of the analyses. Later on, with the aim of observing the eects of taper ratio on aircraft wing
aerodynamic parameters, the revised versions of the wing, which have the taper ratios from 0.2 to 1.2 (with the
increment of 0.2) were analyzed. In conclusion, depending on the analyses results, the wings having dierent
taper ratios were compared in terms of obtained aerodynamic parameters and span-wise lift distributions.
Moreover, tip vortices of each wing, together with their sizes, were obtained and also compared.
Keywords: Aircraft wing design, taper ratio, lift distribution, induced drag coecient.
*Corresponding authour
23rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY,
Eects of Taper Ratio on Aircraft Wing Aerodynamic Parameters: A Comperative Study
kes (RANS) equatons. e am of the analyses was deter-
mnng the wnglet desgn provdng the best aerodynamc
characterstcs. Later on, these analyses were expanded to
complete arcraft and obtaned lft, drag and ptchng mo-
ment coecents were nvestgated together wth wngtp
vortex structures. At the end of the study, they obtaned that
mult wnglet devces were contrbutng on mprovng per-
formance of the arcraft, provdng control on the sprayed
product, reducng the nduced drag and bendng moment
of the wng. Qn et al. [7] performed computatonal ud
dynamcs analyses usng Reynolds-averaged Naver–Stokes
(RANS) equatons on a baselne blended wng body conf-
guraton wth the am of obtanng the eects of span-wse
lft dstrbuton. After the grd senstvty study on total drag,
they obtaned the man factor decreasng the aerodynamc
performance of the baselne body s wng loadng together
wth shock wave. ey revsed the body to three models
havng derent span-wse lft dstrbutons and nvestga-
ted the change n aerodynamc performances. Lee et al. [8]
nvestgated the eect of wnglet dhedral on a tapered and
swept wng at a low Reynolds number. Expermental analy-
ses of the wnglets havng derent dhedral angles were
performed at a wnd tunnel n McGll Unversty at 35 m/s
freestream velocty. Accordng to results of the analyses, t
was obtaned that the nduced-drag of a wng always reduces
wth the use of a wnglet and the wnglet, whch have nega-
tve dhedral, decreases lft-nduced drag more than postve
dhedral. Moreover, t was revealed that, the nner regon
of the tp vortex behavors s smlar for the wng wth or
wthout wnglets.
In ths study, frstly, a hgh aspect rato rectangular arcraft
wng was numercally nvestgated n terms of some ae-
rodynamc parameters ncludng nduced drag coecent,
Oswald ecency factor, and lft coecent together wth
span-wse lft dstrbuton by means of XFLR5 computato-
nal ud dynamcs program. e assessment of mesh accu-
racy of the program was done at the begnnng of the analy-
ses. Later on, wth the am of observng the eects of taper
rato on arcraft wng aerodynamc parameters, the revsed
versons of the wng, whch have the taper ratos from 0.2
to 1.2 (wth the ncrement of 0.2) were analyzed. In conc-
luson, dependng on the analyses results, the wngs havng
derent taper ratos were compared n terms of obtaned
aerodynamc parameters and span-wse lft dstrbutons.
Moreover, tp vortces of each wng, together wth ther s-
zes, were obtaned and also compared.
2.1 Planform Geometry and Aerodynamic Parameters of
an Aircraft Wing
Planform geometry is the top-view shape of a wing and ef-
fective on wing aerodynamic performance [9] [10]. ere-
fore, the geometrical parameters of a wing planform geom-
etry are also important for a wing design. Changing these
geometrical parameters properly with respect to their ef-
fects on the wing aerodynamic parameters can provide an
improved aerodynamic performance to wing. Taper ratio
(λ), as a part of the wing planform geometry, is one of these
important parameters to take into consideration during an
aircraft wing design process. It is the ratio as stated in Equa-
tion (1), which is the ratio of the root (cr) and tip () chord
lengths as shown in Figure 1.
Figure 1: Aircraft wing root and tip chords
e main aerodynamic parameters of an aircraft wing are
drag (CD), lift (CL) and pitching moment (CM) coecients.
e other aerodynamic performance parameters can be de-
rived from these parameters, such as glide ratio, which is the
ratio between lift coecient and drag coecients. Lift, drag
and pitching moment coecients can be calculated using
the Equations (2) - (3) - (4). In these equations, A is the re-
lated area (m2), V is the freestream velocity (m/s), is the lift
force (N), is the drag force (N) and M is the moment (Nm).
On the other hand, drag coecient is divided into two com-
ponents named as zero-lift drag coecient (CDo) and in-
duced drag coecient (CDi) as shown in Equation (4). In the
Equation (5), AR is the wing aspect ratio and e is the Oswald
eciency factor.
CC C=+
AR e
Oswald eciency factor (e) is the value, which gives an idea
about the similarity of a wing’s span-wise lift distribution to
the elliptical lift distribution. e elliptical lift distribution
has Oswald eciency factor of 1 and generally this is the
maximum value of this parameter. ere is another single
parameter, which can represents wing eciency in terms
of induced drag, named as induced drag parameter (δ) and
can be calculated from Equation (6) [11]. is parameter
depends on only planform geometry and independent from
angle of attack and lift coecient.
3rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY,
2.2 Numerical Analyses
e main objective of this study is to investigate the eects
of taper ratio on aerodynamic parameters of a wing design.
In order to examine the eects, rstly, a high aspect ratio
rectangular wing was modelled with a typical sailplane air-
foil named as Wortmann FX 61-184 as a baseline model
[12]. Later on, for the comparison, the baseline model’s ta-
per ratio was revised to 0.2, 0.4, 0.62, 0.8 and 1.2 by changing
tip and root chord lengths while keeping wing area, aspect
ratio and mean geometric chord (M.A.C.) values constant,
as shown in Figure 2.
Figure 2: Planform geometries of revised wing models
Numercal analyses of the sx derent wng models were
performed by XFLR5 program, whch uses Vortex Lattce
Method [13]. On the purpose of obtanng accurate results,
before the analyses, the mesh accuracy of the program was
done on the rectangular model for both drag and lft coe-
cents and results were shown n Fgure 3. Accordng to the
results, all of the models were prepared to have number of
mesh elements hgher than 20000 to have accurate results
ndependent from mesh. e mesh grd of the rectangular
model s shown n Fgure 4. e geometrcal dmensons of
the models, whch were desgned to have sucent number
of mesh elements, were gven n Table 1.
Figure 3: Baseline rectangular model mesh accuracy results
Figure 4: Mesh grid of the rectangular model with 20000 mesh elements
Table 1 Geometrical dimensions of the models
Model Root Chord
Tip Chord
Wing Area
Tap er
1 0.078 0.016
0.047 0.037 16.6
2 0.067 0.027 0.4
3 0.058 0.036 0.62
4 0.052 0.042 0.8
5 0.047 0.047 1
6 0.043 0.051 1.2
Lastly, the models revised from the baseline rectangular
wing model were numerically analyzed at 106 Reynolds
Number. As all the models have high aspect ratios, which is
common on sailplane wing designs, the airspeed was used as
33.5m/s as a typical sailplane cruise speed [14] [15]. As the
stall condition angle of attack or higher values are not scope
of this study, angle of attack range was used as changing be-
tween -6 to 6 degrees [1] [16].
e results of numercal analyses performed on XFLR5
program at 106 Reynolds number n terms of the span-wse
local lft coecents of the models were gven n Fgure 5.
e model 1 (λ=0.2) and model 2 (λ=0.4) have ther hghest
lft coecents near the tp secton of the wng. From model
3 (λ=0.62) to model 6 (λ=1.2), t was clearly seen that the
maxmum lft coecent regon has moved near the mddle
and root secton of the wngs.
Figure 5: Local lift coeicient distributions of the models along their half
Span-wse lft dstrbutons of each model were gven toget-
her wth ther ellptcal lft dstrbutons n Fgure 6. When
the lft dstrbutons of the models were compared wth the-
r ellptcal dstrbutons, near the root secton of the wng,
the lft dstrbuton of the model 3 (λ=0.62) was found to be
most smlar. Moreover, at the regon from the mddle to tp
secton of the wng, model 2 (λ=0.4) was found to have most
smlar lft dstrbuton.
43rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY,
Eects of Taper Ratio on Aircraft Wing Aerodynamic Parameters: A Comperative Study
Figure 6: Span-wise lift distributions with elliptical lift distributions of
the models; a) model 1, b) model 2, c) model 3, d) model 4, e) model 5, f)
model 6
Fgure 7 and Fgure 8 presents the numercal analyss re-
sults of the models n terms of the Oswald ecency factor
and nduced drag parameter. As seen n the fgures, at -6
degree angle of attack, Oswald ecency factors of models
were n order smlar to ther taper ratos. Between the angle
of attacks -4 to 6 degrees, model 2 (λ=0.4) has the hghest
and the model 6 (λ=1.2) has the smallest Oswald ecency
factors. At zero angle of attack, model 1 (e=0.954), model
2 (e=0.977), model 3 (e=0.955) and model 4 (e=0.921) has
Oswald ecency factors hgher than 0.9; model 5 (e=0.884)
and model 6 (e=0.851) has ths values between 0.8 and 0.9.
As expected, nvestgaton of nduced drag parameter of
each model also shows that, model 1 (λ=0.2) and model 3
=0.62) has the same values (δ=0.05). Moreover, they have
very smlar Oswald ecency factor changes at -6 to 6 deg-
rees angles of attacks.
Figure 7: Induced drag parameters (δ) versus taper ratios of the models
3rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY,
Figure 8: Oswald eiciency factors of the models versus angle of attack
from -6 to 6 degrees
In Fgure 9, the numercal results for nduced drag coe-
cents changng wth taper ratos of the models were gven.
As expected, the change of nduced drag coecent valu-
es are n good agreement wth the values of nduced drag
parameter. Model 2 (λ=0.4) has the mnmum (=0.00543)
and model 6 (λ=1.2) has the maxmum value (=0.005886)
of nduced drag coecent. Model 1, 3, 4 and 5 has nduced
drag values of 0.005449, 0.005488, 0.005622 and 0.005806,
Fgure 10 shows the streamlnes of each model at zero angle
of attack at the same dstance from the leadng edges of the
wngs. As seen, the mnmum sze of the wng tp vortces
has seen at model 1 (λ=0.2). e maxmum sze has seen
on model 6 (λ=1.2). erefore, the szes of wng tp vortces
were found to be ncreased wth the decrease n taper rato.
Figure 9: Induced drag coeicients versus taper ratios of the models
e change n total drag coecent wth angle of attack was
gven n Fgure 11. It s seen from the fgure that, model 1
=0.2), has lower drag coecents than other models at
angle of attacks lower than 2 degree. On the contrary, t has
hgher values than other models at angle of attacks hgher
than 2 degree. Models 2, 3, 4, 5 and 6 was found to have s-
mlar changes between angle of attacks of -6 and 6. At zero
angle of attack, models 5 and 6 has approxmately same drag
coecent values of 0.550. Models 1, 2, 3 and 4 has drag co-
ecent values of 0.0521, 0.0528, 0.0538 and 0.0546, respe-
Figure 10: Front-view of streamlines and wing tip vortices of the models
Figure 11: Drag coeicients of models versus angle of attack from -6 to 6
In ths study, wth the am of nvestgatng eects of taper ra-
to on arcraft wng aerodynamc parameters, the hgh aspe-
ct rato wngs havng derent taper ratos were numercally
analyzed. For the comparson of ther aerodynamc parame-
ters, a rectangular wng model was revsed to fve derent
models, whch have derent taper ratos, but have same
wng area, aspect rato and mean aerodynamc chord. Nu-
mercal analyses of the models were performed on XFLR5
program whch uses Vortex Lattce Method. After the as-
sessment of mesh accuracy of the program was done, all
the models havng taper ratos from 0.2 to 1.2 (wth the nc-
rement of 0.2) were analyzed n terms of nduced drag co-
ecent, Oswald ecency factor, and lft coecent toget-
her wth span-wse lft dstrbuton. Accordng to numercal
analyss results, t was obtaned that, there s an optmum
taper rato value for a wng, whch have mnmum nduced
drag coecent and maxmum Oswald ecency factor va-
lues. On the other hand, decreasng taper rato so much was
found to have the possblty of causng wng-tp stall due
to hgher local lft coecents at the tp regon of the wng.
In addton, t was found that, sze of wng-tp vortces were
ncreased wth the ncrease n taper rato.
63rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY,
Eects of Taper Ratio on Aircraft Wing Aerodynamic Parameters: A Comperative Study
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In the agricultural aviation, there are several aerodynamic factors that must be optimized in order to contribute to the successful application of agricultural products, such as the high aerodynamic efficiency (L/D) required at the working phase and the influence of aircraft wingtip phenomena on the spray deposition and movement. For these reasons, in this research is presented the conceptual design of an advanced prototype of agricultural aircraft, whose main characteristic is an adaptive multi-winglet device installed on the wingtips, which optimized the main aerodynamic issues presented in its mission. Traditional aircraft design methods were used to develop and assess the suitability of the aircraft, focusing on its design requirements and tackling studies of weight sizing, pilot ergonomics, aerodynamics, stability, and performance. Subsequently, analytical and computational methods were used to design the adaptive multi-winglet device, which is composed by three winglets with its own geometry fitted on a tip-tank. Six configurations were created by modifying only the cant angle of each winglet in order to determine the arrangement that provides the best aerodynamic characteristics through a study of computational fluid dynamics (CFD), using the Reynolds-Averaged-Navier-Stokes (RANS) equations coupled with the Shear Stress Transport (SST) turbulence model. First, the flow around the wing and the multi-winglet section of the aircraft was investigated exclusively. Afterward, the airflow around the entire aircraft was studied at the product application condition, in order to compare the overall aerodynamic performance of the baseline concept along with the optimal multi-winglet configuration installed on the aircraft. Lift, drag and pitching moment coefficients were assessed, as well as the wingtip vortex structure of the most relevant configurations. Results of this study showed that adaptive multi-winglet devices are a promising alternative to improve the overall performance of an agricultural aircraft, because they provide control over the size and strength of the wake-spray interaction on the sprayed product, reduce the induced drag, reduce the bending moment and improve the aerodynamic efficiency of the aircraft.
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Find the right answer the first time with this useful handbook of preliminary aircraft design. Written by an engineer with close to 20 years of design experience, General Aviation Aircraft Design: Applied Methods and Procedures provides the practicing engineer with a versatile handbook that serves as the first source for finding answers to realistic aircraft design questions. The book is structured in an "equation/derivation/solved example" format for easy access to content. Readers will find it a valuable guide to topics such as sizing of horizontal and vertical tails to minimize drag, sizing of lifting surfaces to ensure proper dynamic stability, numerical performance methods, and common faults and fixes in aircraft design. In most cases, numerical examples involve actual aircraft specs. Concepts are visually depicted by a number of useful black-and-white figures, photos, and graphs (with full-color images included in the eBook only). Broad and deep in coverage, it is intended for practicing engineers, aerospace engineering students, mathematically astute amateur aircraft designers, and anyone interested in aircraft design.
A comprehensive approach to the air vehicle design process using the principles of systems engineering Due to the high cost and the risks associated with development, complex aircraft systems have become a prime candidate for the adoption of systems engineering methodologies. This book presents the entire process of aircraft design based on a systems engineering approach from conceptual design phase, through to preliminary design phase and to detail design phase. Presenting in one volume the methodologies behind aircraft design, this book covers the components and the issues affected by design procedures. The basic topics that are essential to the process, such as aerodynamics, flight stability and control, aero-structure, and aircraft performance are reviewed in various chapters where required. Based on these fundamentals and design requirements, the author explains the design process in a holistic manner to emphasise the integration of the individual components into the overall design. Throughout the book the various design options are considered and weighed against each other, to give readers a practical understanding of the process overall. Readers with knowledge of the fundamental concepts of aerodynamics, propulsion, aero-structure, and flight dynamics will find this book ideal to progress towards the next stage in their understanding of the topic. Furthermore, the broad variety of design techniques covered ensures that readers have the freedom and flexibility to satisfy the design requirements when approaching real-world projects. Key features: Provides full coverage of the design aspects of an air vehicle including: aeronautical concepts, design techniques and design flowcharts Features end of chapter problems to reinforce the learning process as well as fully solved design examples at component level Includes fundamental explanations for aeronautical engineering students and practicing engineers.
The effect of winglet dihedral (-87.5 <= delta <= 87.5 deg) on the near-field tip vortex flow structure behind a swept and tapered NACA 0015 wing was investigated at Re = 1.81 x 10(5). The winglet dihedral led to a significantly reduced (increased) peak tangential velocity and vorticity (core radius) compared to a baseline wing. The values of core circulation (core axial velocity) could be below or above the baseline-wing value, depending on the winglet angle, and exhibited a local maximum (minimum) at delta = 0 deg. The inner region of the tip vortex flow exhibited a self-similar behavior for a wing with and with no winglet. The lift-induced drag was always reduced by the addition of a winglet. The negative dihedral was more effective in reducing the lift-induced drag compared to the corresponding winglet of positive dihedral. A large discrepancy in the lift-induced drag was, however, observed between the wake integral method and the classical lifting-line theory.
This article presents basic results from wing planform optimization for minimum drag with constraints on structural weight and maximum lift. Analyses in each of these disciplines are developed and integrated to yield successful optimization of wing planform shape. Results demonstrate the importance of weight constraints, compressibility drag, maximum lift, and static aeroelasticity on wing shape, and the necessity of modeling these effects to achieve realistic optimized planforms.
For the experimental determination of the dynamic wind tunnel data, a new combined motion test capability was developed at the German–Dutch Wind Tunnels DNW for their 3 m Low Speed Wind Tunnel NWB in Braunschweig, Germany, using a unique six degree-of-freedom test rig called ‘Model Positioning Mechanism’ (MPM) as an improved successor to the older systems. With that cutting-edge device, several transport aircraft configurations including a blended wing body configuration were tested in different modes of oscillatory motions roll, pitch and yaw as well as delta-wing geometries like X-31 equipped with remote controlled rudders and flaps to be able to simulate realistic flight maneuvers, e.g., a Dutch Roll. This paper describes the motivation behind these tests and the test setup and in addition gives a short introduction into time accurate maneuver-testing capabilities incorporating models with remote controlled control surfaces. Furthermore, the adaptation of numerical methods for the prediction of dynamic derivatives is described and some examples with the DLR-F12 configuration will be given. The calculations are based on RANS-solution using the finite volume parallel solution algorithm with an unstructured discretization concept (DLR TAU-code).