AP01_45.vp

1 Introduction
UL aircraft have recently became very popular and rela-

tively simple to build and operate. However this process does
not mean that the design and analysis of such aeroplanes is

unsophisticated. The main aspect, that has an impact on the
design simplicity, is the configuration of lifting surfaces and
its geometry. The L2k is a UL, one-seat, high-wing aeroplane
with an almost parabolic wing layout and mixed construction.
The aeroplane has a tailless configuration with rudders on
the tip of the wing (winglets) and ailerons likewise with a cou-
pled function as a horizontal tail. An aerodynamical analysis
involves investigating the airfoil characteristics for two dif-
ferent values of relative thickness and computations of wing
characteristics. The L2k is designed according to German
BFU requirements for UL aircraft.

2 Notation

Acta Polytechnica Vol. 41 No. 4 – 5/2001

Aerodynamic Design of a Tailless
Aeroplan

J. Friedl

The paper presents an aerodynamic analysis of a one-seat ultralight (UL) tailless aeroplane named L2k, with a very complicated layout. In
the first part, an autostable airfoil with a low moment coefficient was chosen as a base for this problem. This airfoil was refined and modified
to satisfy the design requirements. The computed aerodynamic characteristics of the airfoils for different Reynolds numbers (Re) were
compared with available experimental data. XFOIL code was used to perform the computations. In the second part, a computation of wing
characteristics was carried out. All calculated cases were chosen as points on the manoeuvring and gust envelope. The vortex lattice method
was used with consideration of fuselage and winglets for very complicated wing geometry. The PMW computer program developed at IAE
was used to perform the computations. The computed results were subsequently used for structural and strength analysis and design.

Keywords: aviation, aerodynamics, tailless aeroplane, airfoil, wing.

Fig. 1: L2k layout

Parameter Value Unit
Max. take off weight 300 kg

Length 5.3 m

Height 2.1 m

Total span 11.71 m

Wing span 10.8 m

Dihedral 0 deg
Sweep variable

Wing area 16.8499 m2

Aspect ratio 6.9223 1

Table 1: L2k design parameters

� [deg] Angle of attack

�0 [deg] Zero lift angle

Ck
* [1] Coefficients for wing

CD [1] Drag coefficient

CDi [1] Induced drag coefficient

CL [1] Lift coefficient

CL
�

[rad�1] Lift curve slope

CLmax [1] Max. lift coefficient

CM [1] Moment coefficient (0.25 chord)

CM0as [1] CM of wing for zero lift angle

CM
�

[rad�1] Moment curve slope

�CL
�

[rad�1] CLk difference

�T [deg] Geometric twist angle of wing tip airfoil

�W [deg] Geometric twist angle of winglets

L – Left aileron

n [1] g-loading

R – Right aileron

Re [1] Reynolds number

3 Airfoil analysis
The first step during the design of lifting surfaces is the

choice of an airfoil. An airfoil with low moment coefficient is
needed for tailless aeroplanes to ensure stability during flight.
The N60R airfoil was chosen as the base for further investiga-
tion. This airfoil belongs to the family of autostable profiles
with a slightly “S” shape of the mean curve, which has a direct
impact on the value of the moment coefficient. Because the
original airfoil coordinates were too rough they had to be re-
fined and an airfoil named N60R124 with a relative thickness
of 12.4 % was developed. By modification the N60R124 to
a relative thickness of 15.0 % the N60R150 airfoil arose and
was used at the root wing section. The two airfoils have identi-
cal mean curves with maximum relative camber 2.7 %, so
a similar moment coefficient value was expected.

3.1 Used program
XFOIL version 5.7 code was used to perform the compu-

tations. According to [2] the inviscid formulation built in this
program is a second order panel method with a finite trailing
edge modelled as a source panel. This formulation is closed
with the explicit Kutta-Joukowski condition. The viscous for-
mulation is based on the two-equation lagged dissipation

integral boundary layer model and an envelope en transition
criterion. The solution of the boundary layers and wake
is interacted with the incompressible potential flow via the
surface transpiration model. The drag is computed from the
wake momentum thickness far downstream.

3.2 Experimental data and computation
comparison

At the beginning, the computation for Re = 168 000
was done and compared with available experimental data

from [1]. There was no information about the measurement
conditions, so it was decided to leave the settings of the solu-
tion parameters in XFOIL at default values. The turbulence
intensity was set to 0.07 %. Comparisons for lift and moment
curves are shown in Fig. 3 and 4. For unknown parameters,
e.g. the roughness, turbulence intensity and correction at
measurement space, the comparison was not conclusive.

3.3 Aerodynamic characteristics of airfoils for
different Re numbers

Computations of the aerodynamic characteristics of air-
foils N60R124 and N60R150 were done for the considered
range of Re number for the root and tip section for the
designed speed range and 0 m of ISA. The values of zero
angle attack and lift curve slope were determined by the least
squares method from the lift curves.

80 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 41 No. 4 – 5/2001

Fig. 2: Airfoils N60R124 and N60R150

-5 0 5 10 15 20
-0.2

0.2

0.4

0.6

0.8

1.2

1.4

Re = 168e3 comp.
Re = 168e3 exp.

� [deg]

C
L

[1
]

N60R124

Fig. 3: Lift curve comparison

� [deg]

C
M

[1
]

N60R124

�5 5 10 15 20
�0.08

�0.07

�0.06

�0.05

�0.04

�0.03

�0.02

�0.01

0.01

0.02

Fig. 4: Moment curve comparison

Va [kph] Speed of turn

Vd [kph] Maximum speed

x, y, z coordinate axis

Airfoil N60R124

Airfoil N60R150

Acta Polytechnica Vol. 41 No. 4 – 5/2001

10
5

10
6

10
7

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

C
L

m
a

x
[1

]

N60R124

Re [1]

Fig. 5: Computed variation of CLmax with increasing Re number

Re �0 CL� CLmax
[1] [deg] [rad�1] [1]

168000 �0.36 5.226 1.324

1000000 �0.58 5.998 1.418

2000000 �0.68 6.258 1.511

4000000 �0.83 6.492 1.612

8000000 �1.02 6.642 1.710

Table 2: Aerodynamic characteristics of N60R124, Re range

�5 0 5 10 15 20
�0.5

0.5

1.5

Re = 168e3
Re = 1e6
Re = 2e6
Re = 4e6
Re = 8e6

� [deg]

C
L

[1
]

N60R124

Fig. 6: Computed lift curves

� [deg]

C
M

[1
]

N60R124

�5 0 5 10 15 20
�0.035

�0.03

�0.025

�0.02

�0.015

�0.01

�0.005

0.005

0.01

0.015

Re = 168e3
Re = 1e6
Re = 2e6
Re = 4e6
Re = 8e6

Fig. 7: Computed moment coefficient curves

- 0.5 0 0.5 1 1.5 2
0

0.02

0.04

0.06

0.08

0.1

0.12

Re = 168e3
Re = 1e6
Re = 2e6
Re = 4e6
Re = 8e6

C
D

[1
]

CL [1]

N60R124

Fig. 8: Computed polars

10
6

10
7

1.45

1.5

1.55

1.6

1.65

1.7

C
L

m
a

x
[1

]

N60R150

Re [1]

Fig. 9: Computed variation of CLmax with increasing Re number

3.4 Discussion of results
Airfoils N60R124 and N60R150 can be considered

as suitable for tailless aeroplane due to the low moment
coefficients values. In order to maintain the stability of the
aeroplane a twisted wing tip section and the application of
consistent deflection of the ailerons will be necessary. Experi-
mental data and computation comparison was not applicable
for the set up solution parameters due to unknown measure-
ment conditions.

4 Wing analysis
The structural and strength design of the wing must

take into account the distribution of aerodynamic parameters
along the wing span. This task is quite simple for unswept
wings and can be solved by a wide range of methods based on
Prandtl lift line theory. But for more complex geometry this
task becomes complicated. The L2k aeroplane has a variable
sweep angle due to the parabolic leading and trailing edge
(except ailerons).

4.1 Used program
PMW102 software developed at IAE was used to perform

the computations. This package is based on the Prandtl
theory of lift vortex (panel method) [3, 4]. The lift surface
is replaced by the system of lift vortices distributed along
the span and chord. Two conditions must be satisfied in order
to determine the circulation – tangential flow at the panel
surface and zero value of circulation at the trailing edge
(Kutta–Joukowski condition). The model is divided into
a finite number of trapezoidal panels with a horseshoe system
of vortices. There is a constrained vortex at 1/4 of the panel
chord and free vortices flow from the constrained to the
infinity parallel to the velocity vector. The flow vector must be
tangential to the panel surface at a control point located at 3/4
of the panel chord. This method is appropriate for swept
wings, for lift surfaces with a small aspect ratio and likewise
for complex geometry surfaces. Program allows the model
geometry to be inputted only by the man curve of all bodies.
Only a linear lift curve is considered. The PMW102 package

82 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 41 No. 4 – 5/2001

Re �0 CL� CLmax

[1] [deg] [rad�1] [1]

1000000 �0.62 6.329 1.498

2000000 �0.74 6.541 1.548

4000000 �0.91 6.660 1.608

8000000 �1.02 6.707 1.677

Table 3: Aerodynamic characteristics of N60R150, Re range

�5 0 5 10 15 20
�0.5

0.5

1.5

Re = 1e6
Re = 2e6
Re = 4e6
Re = 8e6

� [deg]

C
L

[1
]

N60R150

Fig. 10: Computed lift curves

�5 0 5 10 15 20
�0.04

�0.03

�0.02

�0.01

0.01

0.02

Re = 1e6
Re = 2e6
Re = 4e6
Re = 8e6

� [deg]

C
M

[1
]

N60R150

Fig. 11: Computed moment coefficient curves

C
D

[1
]

CL [1]

N60R150

- 0.5 0.50
0

1 1.5 2

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Fig. 12: Computed polars

involves a basic pre-processor, a solver and a post-processor,
and is still under development.

4.2 Model geometry
The aeroplane was modelled by the mean curves of all

bodies. This means that the aeroplane geometry was re-
placed by thin surfaces. The fuselage and winglets were also
modelled to find out the impact on the flow field. The wing
geometry had to be simplified because the pre-processor
allows basic trapezoidal wing segments (blocks) to be model-
led so the parabolic wing was replaced by 40 blocks with
refinement at the tip area. A total of 1180 panels were used in
108 sections.

4.3 Investigation process
The first investigation was to determine the geometric

twist angle of the wing tip airfoil (�T). It was derived from the
condition that the difference between the airfoil max. lift
coefficient and the local lift coefficient must be greater than
0.1 in the middle of the aileron span when maximum lift of
the wing is reached. Three variants with twist angles of –2, –3,
–4 degrees were tested and the case ZK 3 (–4 deg.) was chosen
as the best. This variant ensures that flow separation will
develop at the wing root and will extend to the wing tip with
increasing angle of attack. According to the results obtained
a stall speed less than 65 kph (by BFU) will be satisfied.

The next investigation was to determine the geometric
twist angle of the winglets (�w). Three additional variants of
winglet twist angle were studied for the twist variant ZK 3
(Tab. 5). The variant WZK 13 that has the highest value of lift
curve slope is the best from the induced drag point of view.
Nevertheless, based on local CL distribution along the span
(Fig. 14) the variant WZK 33 was chosen, because it gives more
lift in the aileron area.

Acta Polytechnica Vol. 41 No. 4 – 5/2001

Fig. 13: Axonometric view of the computation model

Var. �T CLkmax CMk � Stall Speed

[deg] [1] [1] [deg] [kph]

ZK 1 �2 1.2846 �0.012 17.6 56.246

ZK 2 �3 1.2766 �0.011 18.0 56.421

ZK 3 � 4 1.2139 �0.008 18.0 57.861

Note: CMk is computed towards the y axis. The angle of attack is
measured from the root chord.

Table 4: Tip twist variations

0 1 2 3 4 5 6
- 0.2

- 0.15

- 0.1

- 0.05

0.05

0.1

0.15

0.2

WZK 1 3
WZK 2 3
WZK 3 3

y [m]

C
L

[1
]

Fig. 14: Winglets variants, local CL along span, angle of attack
2 deg

Var. �w �0 CL� �CL�
[deg] [deg] [rad�1] [rad�1]

WZK 13 0 0.9692 4.2124 0

WZK 23 4 1.0830 4.1920 �0.0204

WZK 33 6 1.1475 4.1755 �0.0165

Table 5: Winglet twist angle variants

4.4 Computed cases for strength analysis
The geometric variant WZK 33 was chosen as final to

compute cases for the strength analysis. Five cases were
selected on the manoeuvring and gust envelope (see Tab. 6).
The lift curve was considered linear. This simplification can be
used for the strength analysis.

The wing coefficients CLk and CMk (see Tab. 7) were
computed from the distribution of local values along the span

using the trapezoidal method of numerical integration. The
basic text output from the PMW102 programme with all op-
erational load data is available.

5 Conclusions

The main objectives of the project were successfully
completed. The characteristics of the modified N60R airfoil
were obtained and data for the strength analysis of the wing
was determined. It was shown that relatively complex wing
geometry should be analysed via the panel method approach.
In the investigative process some problems occurred, such as
data evaluation of the results from PMW102, because the
development of this software is still in progress.

References
[1] Horejší, M.: Aerodynamika létajících modelů. Praha, Naše

Vojsko, 1957

[2] Drela, M.: XFOIL User Guide. MIT Aero & Astro Harold
Youngren, Aerocraft, Inc., 2001

[3] Kuthe, A. M., Chow, Ch.: Foundations of aerodynamics.
New York, John Wiley & Sons, Inc., 1998

[4] Brož, V.: Aerodynamika nízkých rychlostí. Ostrava, České
vysoké učení technické v Praze, 1990

Ing. Jan Friedl
phone: +420 5 41143470
fax: +420 5 41142879
e-mail: friedl@iae.fme.vutbr.cz

Institute of Aerospace Engineering
Brno University of Technology
Technická 2, 616 69 Brno, Czech Republic

Acta Polytechnica Vol. 41 No. 4 – 5/2001

Case Speed Speed
value

n Aileron deflection
[deg]

Note

[kph] [1] R L

P1 Va 112.17 4 0 0

P2 Va 112.17 1 �30 20 Full defl.

P3 Vd 210 4 0 0

P4 Vd 210 1 �10 6.67 1/3 defl.

P5 Vd 210 �1.5 0 0

Table 6: Envelope cases

Case � CLk CMk

[deg] [1] [1]

P1 18.500 1.2920 �0.0156

P2 5.617 0.2860 0.0092

P3 6.205 0.3823 �0.0098

P4 2.410 0.0895 0.0011

P5 �1.000 �0.1362 �0.0041

Table 7: Summary of results

0 1 2 3 4 5 6

- 0.5

0.5

1.5

CLmax airf.
P1
P3
P5

y [m]

C
L

[1
]

Symmetrical cases

Fig. 15: Local CL along span, symmetrical cases

- 6 - 4 - 2 0 2 4 6
- 1

- 0.8

- 0.6

- 0.4

- 0.2

0.2

0.4

0.6

0.8

P2
P4

y [m]

C
L

[1
]

Unsymmetrical cases

Fig. 16: Local CL along span, unsymmetrical cases

�0 CM0as CL� CM�

[deg] [1] [rad�1] [rad�1]

WZK 33 1.1475 �0.0053 4.1755 �0.0286

Table 8: Results in linear area of lift curve