Acta Polytechnica


doi:10.14311/AP.2017.57.0001
Acta Polytechnica 57(1):1–7, 2017 © Czech Technical University in Prague, 2017

available online at http://ojs.cvut.cz/ojs/index.php/ap

AN AIRPLANE WITH UNCONVENTIONALLY PLACED
PROPELLER POWER UNITS

Jan Červinka, Robert Kulhánek∗, Zdeněk Pátek
VZLÚ a.s. — Aerospace Research and Test Establishment, Beranových 130, Prague, Czech Republic

∗ corresponding author: kulhanek@vzlu.cz

Abstract. The significance of the influence of operating propellers on the aircraft aerodynamic
characteristics is well-known. Wind tunnel testing of an airplane model with operating propellers is a
complex task regarding the required similarity of the full-scale and the model case. Matching sufficient
similarity in axial and rotational velocities in the propeller slipstream is the primordial condition for
the global aerodynamic similarity of the windtunnel testing. An example of the model power units
with related devices is presented. Examples of the wind tunnel testing results illustrate the extent of
the propeller influence on aerodynamic characteristics of an aircraft of unconventional configuration
with power units positioned at the fuselage afterbody.
Keywords: windtunnel testing; propeller slipstream; T-tail aircraft; propeller simulation.

1. Introduction
The simulation of the propeller effects is an important
part of the wind tunnel testing of an airplane. Both
the importance and the complexity of the simulation
are given by the fact that the aerodynamic phenomena
connected with a propeller are very complex including
complex interactions between the propeller(s) and the
airframe.

2. Review of current research
The first scientific studies treating the influence of the
propeller on the aerodynamics and flight mechanics of
an airplane were published as early as in the thirties
of the last century, in relationship with the increasing
power of the installed engines and the spreading of
the multi-engine aircraft [1–3]. Especially, Millikan’s
study [4] is considered as a principal fundament with
many other authors continuing and developing it in
specific areas (as for example [5]). These works are
based mainly on the empirical expressions considering
the power-on propeller downwash and the tail in the
slipstream; these expressions are developed from the
results of the wind tunnel testing. The importance
of the mutual position of the propeller with its slip-
stream and the wing and the horizontal tailplane was
perceived as well as the influence of the sense of the
rotation of the propeller. But the above mentioned
classical studies are focused on the conventional con-
figuration of an airplane, i.e., the tractor propellers
positioned ahead of the leading edge of the wing and
the horizontal tailplane on the fuselage or in the prox-
imity of the fuselage. There are many other studies
focused on the propeller-wing interference (even in the
last period, for example [6, 7]), but this phenomenon
is not the main topic of this paper.

The studies devoted to the propeller influence have
appeared during the decades, but none of them specifi-
cally focused on the studied configuration. The global

survey of the available literature sources up to 1985 is
given in [8].This survey contains abstracts and excerp-
tions from 121 sources and confirms that the uncon-
ventional configurations have been out of the interest
of the most studies. The main interest of the recent
studies consisted in the critical case with one engine
inoperative on a twin-engine aircraft (for example
[9–11]) , i.e., the aim is the examination of the influ-
ence of propeller and its slipstream especially on the
directional stability and controllability.

The twin-engine aircraft with aft placed propellers
are rare but have been existing and successfully flying.
Their designers undoubtedly had to cope with the
problems of the influence of the propellers, but the
details about their aerodynamics and flight mechanics
do not seem to be available in open literature. One
exemption is [12] which includes among others data
concerning configuration with pusher propellers on the
wing but it is configuration is totally different from
the studied configuration with pusher power units on
the rear of the fuselage.
The presented study intends to fill the gap in the

understanding of the influence of the propellers on
the unconventional twin-engine configuration of an
airplane that is characterized by the two propellers
on the rear of the fuselage and by the T-tail. It was
supposed that the influence on the wing was marginal
but influence on the tail and thus longitudinal and
directional stability and controllability could be sig-
nificant.
As was published in [11, 13] for the conventional

twin-engine configuration, the yawing moment with
one engine inoperative is not a simple thrust of the
operative engine multiplied by its arm to the centre
of gravity. In addition to it, there is a complex aero-
dynamic interaction, especially between the propeller
slipstream and the fuselage and primarily the vertical
tailplane that causes that the total yawing moment is
approximately 50 percent higher.

1

http://dx.doi.org/10.14311/AP.2017.57.0001
http://ojs.cvut.cz/ojs/index.php/ap


J. Červinka, R. Kulhánek, Z. Pátek Acta Polytechnica

3. Motivation
The importance of the influence of the operating pro-
peller power units on aircraft aerodynamic character-
istics is well-known. The propeller units create both
direct effects caused by the forces acting directly at the
propeller (thrust, normal force, torque moment) and
indirect effects caused by the significant aerodynamic
influence on the aircraft and on the flow circumventing
the airframe. This influence is caused primarily by
the interaction of the propeller slipstream with other
parts of the aircraft.
It is also evident that the influence depends essen-

tially on the power output of the power unit; the
higher power output, the higher direct forces but also
the higher “indirect” aerodynamic influence as the
strength of the slipstream is related to the forces cre-
ated at the propeller. The power is often usefully
relative to the size of the aircraft, the relation can be
conveniently expressed for example using power-to-
mass ratio of an aircraft. The effects of the propeller
on the wing or on the whole aircraft are well-described
in the case of the conventional propeller-driven air-
craft configuration, i.e., in the case of a single-engine
aircraft with propeller on the nose of the fuselage and
in the case of a multi-engine aeroplane with propellers
in front of the leading edge of the wing.

But the experimental results for the unconventional
configuration with propellers positioned on the rear
part of the fuselage behind the wing and in the prox-
imity of the tail surfaces have not been found in the
available literature sources. As the both direct and
indirect propeller effects influence not only the aircraft
aerodynamics but also its flight dynamics behaviour
as one of main consequences, therefore the simulation
of the propeller effects at wind tunnel testing of an
airplane is very important. Especially the influence
on aircraft stability and controllability can be crucial.

4. Theory of similarity
4.1. Propeller effects
The most significant direct and indirect effects are as
follows.
(1.) Direct effects

• Thrust in the axis of the propeller
• Normal force in the plane of rotation of the pro-

peller
• Torque moment of the propeller

(2.) Indirect effects of the propeller slipstream
• Effect on the moments of the wing
• Effect on the lift of the wing
• Effect on the downwash and the crossflow at the
tail unit

• Effect on the dynamic pressure at the tail unit
The simulation of the propeller slipstream for a

constant-speed propeller requires matching both the

slipstream axial velocity-to-airspeed and the slip-
stream rotational velocity-to-airspeed ratios. But to
match these both ratios over the entire range of the
aircraft lift coefficients would require an adjustable
pitch propeller, in ideal case adjustable “in flight” dur-
ing testing run and that is a very challenging issue.
However, a satisfactory approximation of the real slip-
stream can be accomplished with a single setting of
a propeller pitch (or very limited number of settings)
over a large part of the lift coefficients, so manually
“on ground” adjustable propeller is sufficiently ade-
quate for the wind tunnel testing.

From propeller momentum theory, it can be found
that the axial velocity ratio can be matched with a
propeller of a scale diameter. The rotational velocity
ratio can be matched with a geometrically similar
propeller operating at the proper advance ratio.
To match required similarity in the thrust and

torque, the equality of the full-scale TcFS and the
model TcM and of the QcFS and QcM coefficients shall
be matched.

It is possible to deduce, if the full-scale and model
propellers are geometrically similar, that for a given
propeller advance ratio (identical for both the full-
scale and model propellers JM = JF), the correct
similarity of the thrust is preserved when TcM =
TcFS. In a similar manner, the similarity of the torque
moment is preserved when QcM = QcFS see example
Pope [14] for the deduction that we present in the
brief form.
The conditions of similarity suppose that the geo-

metrically similar propellers, at a given advance ratio,
have identical CTFS and CTM (and analogically CQFS
and CQM) coefficients, which is not exactly matched
in reality because of very different propeller Reynolds
numbers and different propeller Mach numbers. The
model to the full-scale Reynolds numbers ratio is given
by the ratio of the wind tunnel flow velocity to the
flight airspeed multiplied by the geometric scale factor,
the Mach numbers ratio is given by the ratio of the
wind tunnel flow velocity to the flight airspeed. The
partial correction can be achieved by model propeller
design, the propeller is not designed in practice as ex-
actly geometrically similar to the full-scale propeller;
it keeps the correct scale diameter and the number
of blades, whereas the airfoil sections of the blades
are different, taking into account the differences of
the Reynolds and Mach numbers. The result of the
proper model propeller design is that the differences
in the thrust and torque coefficients between the full-
scale and the model propellers are negligible from
the practical point of view if the low-speed testing is
performed in the linear region of the propeller charac-
teristics (i.e., in the linear regions of CT vs J and CQ
vs J curves).

In practice, there is limited amount of regimes of the
flight to be tested, the maximum power unit (take-off)
regime and the cruise regime are usually examined.
It is possible to design the propeller model in a way

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Figure 1. Schematic sketch of tested configuration.

Figure 2. Schematic sketch of REF. 1 configuration.

Figure 3. Schematic sketch of REF. 2 configuration.

(take-off) regime and the cruise regime are usually
examined. It is possible to design model propeller
that is aerodynamically sufficiently similar at one
selected blade incidence to the full-scale propeller
in these regimes. With the appropriately designed
model propeller, the thrust coefficient can be matched
exactly and, simultaneously, the torque coefficient can
be matched with the discrepancy of several percent,
i.e. within acceptable limits.

4.2. Model and testing device
An experimental wind tunnel testing was performed
with a generic model of a small low-wing monoplane
with T-tail and with two propellers positioned at the
rear part of the fuselage. To emphasize the effects
connected with the propeller, the propeller diame-
ter was relatively big and the thrust coefficient of
the power units relatively high. The propellers could
rotate either in the identically oriented senses (the
both clockwise viewed from the rear, the green ar-
row in Figure 1 either in counter-rotating mode (the
left propeller clockwise, the right propeller counter-
clockwise).
The model propellers were driven by electric mo-

tors built in the models of the engine nacelles. The
model propeller has a diameter of 0.4m and was pow-
ered by electronic engines with a maximum power of
16kW at 11000 rpm. This value of the advance ratio
corresponds to take-off regime.

Figure 4. Wind tunnel.

The results of the unconventional configuration was
compared with one conventional configuration and
one unconvential of different type. The conventional
airplane is a small low-wing monoplane with conven-
tional tail and two propellers placed in front of the
wing. The layout this configuration can be seen in
Figure 2 and the wind tunnel testing is described in
reference [15]. The second unconventional configura-
tion is a low-wing monoplane from reference [16]. The
layout of this configuration is similar but with engines
placed above the horizontal tail unit. The sketch of
this configuration can be seen in Figure 3.
The tests were carried out in a low-speed closed

circut atmospheric wind tunnel operaited by VZLU
Aerospace Research and Test Establishment in Prague.
The wind tunnel has the following main characteris-
tics.
• Circural test section of 3 m.
• Maximum velocity 75 m/s (with ventilation), 90m/s
(without ventilation)

• Characteristic turbulence intensity 0.3 %.
The wind tunnel sketch can be seen in Figure 4.

5. Results
The results of the wind tunnel testing are presented
in Figure 5 to Figure 9. The testing with operating
propellers was performed at Reynolds number 900,000
(related to the wing mean aerodynamic chord). The
thrust coefficient of one propeller Tc was kept constant
regardless the angle of attack of the airplane model.

3

Figure 1. Schematic sketch of tested configuration.

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Figure 1. Schematic sketch of tested configuration.

Figure 2. Schematic sketch of REF. 1 configuration.

Figure 3. Schematic sketch of REF. 2 configuration.

(take-off) regime and the cruise regime are usually
examined. It is possible to design model propeller
that is aerodynamically sufficiently similar at one
selected blade incidence to the full-scale propeller
in these regimes. With the appropriately designed
model propeller, the thrust coefficient can be matched
exactly and, simultaneously, the torque coefficient can
be matched with the discrepancy of several percent,
i.e. within acceptable limits.

4.2. Model and testing device
An experimental wind tunnel testing was performed
with a generic model of a small low-wing monoplane
with T-tail and with two propellers positioned at the
rear part of the fuselage. To emphasize the effects
connected with the propeller, the propeller diame-
ter was relatively big and the thrust coefficient of
the power units relatively high. The propellers could
rotate either in the identically oriented senses (the
both clockwise viewed from the rear, the green ar-
row in Figure 1 either in counter-rotating mode (the
left propeller clockwise, the right propeller counter-
clockwise).
The model propellers were driven by electric mo-

tors built in the models of the engine nacelles. The
model propeller has a diameter of 0.4m and was pow-
ered by electronic engines with a maximum power of
16kW at 11000 rpm. This value of the advance ratio
corresponds to take-off regime.

Figure 4. Wind tunnel.

The results of the unconventional configuration was
compared with one conventional configuration and
one unconvential of different type. The conventional
airplane is a small low-wing monoplane with conven-
tional tail and two propellers placed in front of the
wing. The layout this configuration can be seen in
Figure 2 and the wind tunnel testing is described in
reference [15]. The second unconventional configura-
tion is a low-wing monoplane from reference [16]. The
layout of this configuration is similar but with engines
placed above the horizontal tail unit. The sketch of
this configuration can be seen in Figure 3.
The tests were carried out in a low-speed closed

circut atmospheric wind tunnel operaited by VZLU
Aerospace Research and Test Establishment in Prague.
The wind tunnel has the following main characteris-
tics.
• Circural test section of 3 m.
• Maximum velocity 75 m/s (with ventilation), 90m/s
(without ventilation)

• Characteristic turbulence intensity 0.3 %.
The wind tunnel sketch can be seen in Figure 4.

5. Results
The results of the wind tunnel testing are presented
in Figure 5 to Figure 9. The testing with operating
propellers was performed at Reynolds number 900,000
(related to the wing mean aerodynamic chord). The
thrust coefficient of one propeller Tc was kept constant
regardless the angle of attack of the airplane model.

3

Figure 2. Schematic sketch of REF. 1 configuration.

that it is aerodynamically sufficiently similar at one
selected blade incidence to the full-scale propeller
in these regimes. With the appropriately designed
the propeller, the thrust coefficient can be matched
exactly and, simultaneously, the torque coefficient can
be matched with the discrepancy of several percent,
i.e., within acceptable limits.

4.2. Model and testing device
An experimental wind tunnel testing was performed
with a generic model of a small low-wing monoplane
with T-tail and with two propellers positioned at the
rear part of the fuselage. To emphasize the effects
connected with the propeller, the propeller diameter
was relatively big and the thrust coefficient of the
power units relatively high. The propellers could
rotate either in the identically oriented senses (the
both clockwise viewed from the rear, the green arrow
in Figure 1 either on in counter-rotating mode (the
left propeller clockwise, the right propeller counter-
clockwise).
The model propellers were driven by electric mo-

tors built in the models of the engine nacelles. The
model propeller has a diameter of 0.4m and was pow-
ered by electronic engines with a maximum power of
16 kW at 11000 rpm. This value of the advance ratio
corresponds to the take-off regime.

The results of the unconventional configuration were
compared with one conventional configuration and one
unconventional configuration of a different type. The
conventional airplane is a small low-wing monoplane
with a conventional tail and two propellers placed in
front of the wing. The layout of this configuration
can be seen in Figure 2 and the wind tunnel testing
is described in reference [15]. The second one, the
unconventional configuration is a low-wing monoplane

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Figure 1. Schematic sketch of tested configuration.

Figure 2. Schematic sketch of REF. 1 configuration.

Figure 3. Schematic sketch of REF. 2 configuration.

(take-off) regime and the cruise regime are usually
examined. It is possible to design model propeller
that is aerodynamically sufficiently similar at one
selected blade incidence to the full-scale propeller
in these regimes. With the appropriately designed
model propeller, the thrust coefficient can be matched
exactly and, simultaneously, the torque coefficient can
be matched with the discrepancy of several percent,
i.e. within acceptable limits.

4.2. Model and testing device
An experimental wind tunnel testing was performed
with a generic model of a small low-wing monoplane
with T-tail and with two propellers positioned at the
rear part of the fuselage. To emphasize the effects
connected with the propeller, the propeller diame-
ter was relatively big and the thrust coefficient of
the power units relatively high. The propellers could
rotate either in the identically oriented senses (the
both clockwise viewed from the rear, the green ar-
row in Figure 1 either in counter-rotating mode (the
left propeller clockwise, the right propeller counter-
clockwise).
The model propellers were driven by electric mo-

tors built in the models of the engine nacelles. The
model propeller has a diameter of 0.4m and was pow-
ered by electronic engines with a maximum power of
16kW at 11000 rpm. This value of the advance ratio
corresponds to take-off regime.

Figure 4. Wind tunnel.

The results of the unconventional configuration was
compared with one conventional configuration and
one unconvential of different type. The conventional
airplane is a small low-wing monoplane with conven-
tional tail and two propellers placed in front of the
wing. The layout this configuration can be seen in
Figure 2 and the wind tunnel testing is described in
reference [15]. The second unconventional configura-
tion is a low-wing monoplane from reference [16]. The
layout of this configuration is similar but with engines
placed above the horizontal tail unit. The sketch of
this configuration can be seen in Figure 3.
The tests were carried out in a low-speed closed

circut atmospheric wind tunnel operaited by VZLU
Aerospace Research and Test Establishment in Prague.
The wind tunnel has the following main characteris-
tics.
• Circural test section of 3 m.
• Maximum velocity 75 m/s (with ventilation), 90m/s
(without ventilation)

• Characteristic turbulence intensity 0.3 %.
The wind tunnel sketch can be seen in Figure 4.

5. Results
The results of the wind tunnel testing are presented
in Figure 5 to Figure 9. The testing with operating
propellers was performed at Reynolds number 900,000
(related to the wing mean aerodynamic chord). The
thrust coefficient of one propeller Tc was kept constant
regardless the angle of attack of the airplane model.

3

Figure 3. Schematic sketch of REF. 2 configuration.

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Figure 1. Schematic sketch of tested configuration.

Figure 2. Schematic sketch of REF. 1 configuration.

Figure 3. Schematic sketch of REF. 2 configuration.

(take-off) regime and the cruise regime are usually
examined. It is possible to design model propeller
that is aerodynamically sufficiently similar at one
selected blade incidence to the full-scale propeller
in these regimes. With the appropriately designed
model propeller, the thrust coefficient can be matched
exactly and, simultaneously, the torque coefficient can
be matched with the discrepancy of several percent,
i.e. within acceptable limits.

4.2. Model and testing device
An experimental wind tunnel testing was performed
with a generic model of a small low-wing monoplane
with T-tail and with two propellers positioned at the
rear part of the fuselage. To emphasize the effects
connected with the propeller, the propeller diame-
ter was relatively big and the thrust coefficient of
the power units relatively high. The propellers could
rotate either in the identically oriented senses (the
both clockwise viewed from the rear, the green ar-
row in Figure 1 either in counter-rotating mode (the
left propeller clockwise, the right propeller counter-
clockwise).
The model propellers were driven by electric mo-

tors built in the models of the engine nacelles. The
model propeller has a diameter of 0.4m and was pow-
ered by electronic engines with a maximum power of
16kW at 11000 rpm. This value of the advance ratio
corresponds to take-off regime.

Figure 4. Wind tunnel.

The results of the unconventional configuration was
compared with one conventional configuration and
one unconvential of different type. The conventional
airplane is a small low-wing monoplane with conven-
tional tail and two propellers placed in front of the
wing. The layout this configuration can be seen in
Figure 2 and the wind tunnel testing is described in
reference [15]. The second unconventional configura-
tion is a low-wing monoplane from reference [16]. The
layout of this configuration is similar but with engines
placed above the horizontal tail unit. The sketch of
this configuration can be seen in Figure 3.
The tests were carried out in a low-speed closed

circut atmospheric wind tunnel operaited by VZLU
Aerospace Research and Test Establishment in Prague.
The wind tunnel has the following main characteris-
tics.
• Circural test section of 3 m.
• Maximum velocity 75 m/s (with ventilation), 90m/s
(without ventilation)

• Characteristic turbulence intensity 0.3 %.
The wind tunnel sketch can be seen in Figure 4.

5. Results
The results of the wind tunnel testing are presented
in Figure 5 to Figure 9. The testing with operating
propellers was performed at Reynolds number 900,000
(related to the wing mean aerodynamic chord). The
thrust coefficient of one propeller Tc was kept constant
regardless the angle of attack of the airplane model.

3

Figure 4. Wind tunnel.

from reference [16]. The layout of this configuration is
similar but with engines placed above the horizontal
tail unit. The sketch of this configuration can be seen
in Figure 3.
The tests were carried out in a low-speed closed

circut atmospheric wind tunnel operaited by VZLU
Aerospace Research and Test Establishment in Prague.
The wind tunnel has the following main characteris-
tics.
• Circural test section of 3m.
• Maximum velocity 75m/s (with ventilation), 90m/s
(without ventilation)

• Characteristic turbulence intensity 0.3%.
The wind tunnel sketch can be seen in Figure 4.

5. Results
The results of the wind tunnel testing are presented
in Figure 5 to Figure 9. The testing with operating
propellers was performed at Reynolds number 900,000
(related to the wing mean aerodynamic chord). The
thrust coefficient of one propeller Tc was kept constant
regardless the angle of attack of the airplane model.

3



J. Červinka, R. Kulhánek, Z. Pátek Acta Polytechnica

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Jan. Červinka, R. Kulhánek, Z. Pátek Acta Polytechnica
PREPRINT 2016-09-19

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The results are compared with the conventional con-
figuration (in the figure legend are marked as REF.1)
and some of them with unconventional one (REF. 2).
As was published in [11] [13] for the conventional

twin-engine configuration, the yawing moment with
one engine inoperative is not a simple product of the
thrust of the operative engine multiplied by its arm to
the centre of gravity. In addition to it, there is com-
plex aerodynamic interaction, especially between the
propeller slipstream and the fuselage and primarily
the slipstream and the vertical tailplane that causes
that the total yawing moment is approximately 50
percent higher. This phenomenon yields important
influence on the directional stability and controlla-
bility. The influence of one engine operative on the
studied configuration reveals to be more complex as it
surprisingly strongly depends on the sense of rotation
of the propeller.

With the propeller blades moving from-up-to-down
in the proximity of the vertical tailplane (i.e. clockwise
turning on the left engine), the result is of the similar
nature as in the case of the conventional configura-
tion: the resulting yawing moment is approximately
1.25 higher than the product of the engine thrust
and its arm. With the opposite sense of rotation (i.e.
counter-clockwise on the left engine), the yawing mo-
ment diminish to nearly zero, i.e. the aerodynamic
interference practically wipe out the moment created
by the engine thrust multiplied by its arm. It seems
to be significant finding. However, with possible but
in practice probably limited impact. It implies that
desirable reduction of the vertical tailplane and rud-
der could be possible but the real exploitation of it
would necessitate the opposite senses of rotation of the
engines and thus two different versions of the engine
with different gearboxes.

From the point of view of the flow physics, it in-
dicates strong interaction between the propeller and
the vertical tailplane and (maybe) the wing wake but
the exact nature of it remains to be clarified in detail.
Set of flow visualizations on the rear part of the fuse-
lage and on the vertical tailplane were performed but
without registration of any significant difference.

6. Discussion
6.1. Influence of propellers on lift
Detectable difference is observed between the two
cases of the propeller rotation. The slope of the both
lift curves is almost identical, but CL0 for the counter-
rotating propellers is slightly lower, 4CL0 ≈ −0.02.
The explanation is probably in the flow over the hori-
zontal tailplane, as its right side was influences mainly
by counterclockwise rotating propeller which rather
decreases the angle of attack. In general, the position
of the propeller above and under horizontal surface,
does not change significantly slope of the lift curve.
The influence of the propellers placed on the wing

(REF. 1) is more significant. The increment 4CL0 ≈

�
�

�I

�TVo

T

TVo

I

IVo

A

	−��

�IT T IT AT

��������������−O−�����−���
��������������−O−�����−��
��������������−O−�����−�����
�� V−I−O−�����−���
�� V−I−O−�����−��
�� V−A−O−�����−���
�� V−A−O−�����−��

Figure 5. Lift curves.

0.1 is much higher than has the non conventional
configuration. Higher increment of the lift coefficient is
due to the fact that the propeller slipstream increases
the local velocity around small portion of the wing
behind propeller. The explanation for the higher lift
curve slope of the conventional configuration can be
found also in this phenomenon.

6.2. Influence of propellers on static
longitudinal stability of aeroplane
without horizontal tail surface

The direct effect of the thrust is removed from the
pitching moment characteristics by positioning of the
centre of gravity placed in the thrust line. The refer-
ence points has identical longitudinal distance relative
to the mean aerodynamic cord for all tested configu-
ration. It is evident that the presence of the power
units has the stabilizing effect. The neutral point
moves backward approximately 8 percent of the mean
aerodynamic cord for unconvential configuration and
approximately 1 percent for the REF. 1 one. The
conventional configuration has the nose down pitching
moment. The explanation is that the increased ve-
locity over part of the wing magnify the wing pitchig
moment. The significant effect of the power units on
static stability of the unconventional configuration
can be explained as stabilizing effect of propeller nor-
mal force. The pitchig moment of the unconventional
configuration differs around zero angle of attack where
the propeller normal force supposed to be zero it can
be resumed that this nose-up pitchig moment has to
be product of changes in flowfield near pylons of the
nacelle.

4

Figure 5. Lift curves.

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��������
��	
�����
�2�i i�����i���
��	
�����
�2�i i�����i��iV�iwooNE
���-wi i�����i���
���-wi i�����i��

	
!

"o-(

"o-r(

o

o-r(

o-(

o-1(

	�

"w "o-( o o-( w w-( r

Figure 6. Moment curves of tailless aircraft.

6.3. Influence of propellers on static
longitudinal stability of complete
aeroplane

The influence of the rotating propellers on the hori-
zontal tailplane is pronounced as longitudinal desta-
bilization of the aeroplane. The neutral point moved
forward by approximately 5 percent of the mean aero-
dynamic chord with the propellers rotating in the
identical senses, and by approximately 1 percent with
the counter-rotating propellers. With respect to the
fact that the propellers have opposite influence than
for the aircraft without the horizontal taill, it seems
possible to deduce that there is very significant influ-
ence of the propellers on the horizontal tail, regardless
the geometrical fact that the horizontal tailplane is
positioned high above the propellers and only slightly
behind the plane of the propeller discs. The propellers
creates such changes in the flowfield that in conse-
quence led to the decreasing of the angle of attack of
the horizontal tailplane and thus to the diminution of
its lift (with respect to the convention that positive
lift was directed “upwards”). This influence is even
more pronounced for the counter-rotating propellers.
The almost constant nose-up pitching moment is

produced by the increased velocity under the horizon-
tal tail surface. Simillar phenomenon was reported in
reference [16] also. In that study, the aircraft with the
power units placed above the horizontal tail surface
was tedsted in the wind tunnel. This configuration is
marked as REF.2 in Figure 7. and it can be observed
that the power units has stabilizing effect and add
nose-down pitching moment. The neutral point moves
backward by approximately 3 percent of the mean
aerodynamic chord.
The rotating propellers of the conventional config-

uration has adverse effect on the longitudinal static
stability. The neutral point moved forward by approx-

����
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ipi�����i���
�����	
�����7
ipi�����i��iI�ireeOA
�����	
�����7
ipi�����i�����iI�ireeOA
�
�oripi�����i���
�
�oripi�����i��
�
�ofipi�����i���
�
�ofipi�����i��

�
!

"eoP

"eofP

e

eofP

eoP

eo0P

�

"r "eoP e eoP r roP f

Figure 7. Moment curves of complete aircraft.

imately 12 percent of the mean aerodynamic chord.
It can be seen that the power effect change the static
margin without tail minimally so it can be deduced
that the propeller slipsteam change the downwash
behind the wing and the horizontal stabilizer is less
effective.

6.4. Influence of propellers on static
lateral-directional stability

6.4.1. Roll
The rotation of the propellers increases the “lateral sta-
bility”, i.e. increases the absolute value of the deriva-
tive of the rolling moment with respect to the sideslip
angle. The increase is approximately 16 percent with
the both propellers rotating clockwise and 12 percent
with counter-rotating propellers. The probable reason
is the difference between force components at the left
and the right propellers discs created as a result of
combination of the angle of attack and the sideslip
angle. This phenomenon is slightly supressed by the
counter-rotating propellers. The reaction torque mo-
ment of the clockwise rotating propellers also causes
the negative rolling moment at the zero sideslip angle.
The moment is relatively high as its value correspon-
des to the sideslip of 4 degrees.
The placement of the propeller on aircraft wing

has negligible effect on the lateral stability the shift
of the rolling moment coefficient at zero sideslip an-
gle is caused by wind tunnel airstream misalinement
according to reference [15].

6.4.2. Yaw
The influence of the propellers on the derivative of
the yawing moment with respect to the sideslip angle
is also highly pronounced, and the propeller opera-
tion significantly increases its value also in this case.
The increase is approximately 17 percent with the

5

Figure 6. Moment curves of tailless aircraft.

The results are compared with the conventional con-
figuration (in the figure legend marked as REF. 1)
and some of them with unconventional one (REF. 2).
As was published in [11, 13] for the conventional

twin-engine configuration, the yawing moment with
one engine inoperative is not a simple product of the
thrust of the operative engine multiplied by its arm to
the centre of gravity. In addition to it, there is a com-
plex aerodynamic interaction, especially between the
propeller slipstream and the fuselage and, primarily,
between the slipstream and the vertical tailplane that
causes that the total yawing moment is approximately
50 percent higher. This phenomenon yields important
influence on the directional stability and controlla-
bility. The influence of one engine operative on the
studied configuration reveals to be more complex as it

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��������
��	
�����
�2�i i�����i���
��	
�����
�2�i i�����i��iV�iwooNE
���-wi i�����i���
���-wi i�����i��

	
!

"o-(

"o-r(

o

o-r(

o-(

o-1(

	�

"w "o-( o o-( w w-( r

Figure 6. Moment curves of tailless aircraft.

6.3. Influence of propellers on static
longitudinal stability of complete
aeroplane

The influence of the rotating propellers on the hori-
zontal tailplane is pronounced as longitudinal desta-
bilization of the aeroplane. The neutral point moved
forward by approximately 5 percent of the mean aero-
dynamic chord with the propellers rotating in the
identical senses, and by approximately 1 percent with
the counter-rotating propellers. With respect to the
fact that the propellers have opposite influence than
for the aircraft without the horizontal taill, it seems
possible to deduce that there is very significant influ-
ence of the propellers on the horizontal tail, regardless
the geometrical fact that the horizontal tailplane is
positioned high above the propellers and only slightly
behind the plane of the propeller discs. The propellers
creates such changes in the flowfield that in conse-
quence led to the decreasing of the angle of attack of
the horizontal tailplane and thus to the diminution of
its lift (with respect to the convention that positive
lift was directed “upwards”). This influence is even
more pronounced for the counter-rotating propellers.
The almost constant nose-up pitching moment is

produced by the increased velocity under the horizon-
tal tail surface. Simillar phenomenon was reported in
reference [16] also. In that study, the aircraft with the
power units placed above the horizontal tail surface
was tedsted in the wind tunnel. This configuration is
marked as REF.2 in Figure 7. and it can be observed
that the power units has stabilizing effect and add
nose-down pitching moment. The neutral point moves
backward by approximately 3 percent of the mean
aerodynamic chord.
The rotating propellers of the conventional config-

uration has adverse effect on the longitudinal static
stability. The neutral point moved forward by approx-

����
�����	
�����7
ipi�����i���
�����	
�����7
ipi�����i��iI�ireeOA
�����	
�����7
ipi�����i�����iI�ireeOA
�
�oripi�����i���
�
�oripi�����i��
�
�ofipi�����i���
�
�ofipi�����i��

�
!

"eoP

"eofP

e

eofP

eoP

eo0P

�

"r "eoP e eoP r roP f

Figure 7. Moment curves of complete aircraft.

imately 12 percent of the mean aerodynamic chord.
It can be seen that the power effect change the static
margin without tail minimally so it can be deduced
that the propeller slipsteam change the downwash
behind the wing and the horizontal stabilizer is less
effective.

6.4. Influence of propellers on static
lateral-directional stability

6.4.1. Roll
The rotation of the propellers increases the “lateral sta-
bility”, i.e. increases the absolute value of the deriva-
tive of the rolling moment with respect to the sideslip
angle. The increase is approximately 16 percent with
the both propellers rotating clockwise and 12 percent
with counter-rotating propellers. The probable reason
is the difference between force components at the left
and the right propellers discs created as a result of
combination of the angle of attack and the sideslip
angle. This phenomenon is slightly supressed by the
counter-rotating propellers. The reaction torque mo-
ment of the clockwise rotating propellers also causes
the negative rolling moment at the zero sideslip angle.
The moment is relatively high as its value correspon-
des to the sideslip of 4 degrees.
The placement of the propeller on aircraft wing

has negligible effect on the lateral stability the shift
of the rolling moment coefficient at zero sideslip an-
gle is caused by wind tunnel airstream misalinement
according to reference [15].

6.4.2. Yaw
The influence of the propellers on the derivative of
the yawing moment with respect to the sideslip angle
is also highly pronounced, and the propeller opera-
tion significantly increases its value also in this case.
The increase is approximately 17 percent with the

5

Figure 7. Moment curves of complete aircraft.

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Jan. Červinka, R. Kulhánek, Z. Pátek Acta Polytechnica
PREPRINT 2016-09-19

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������������	
CeC
����C���
������������	
CeC
����C��
������������	
CeC
����C�����

���CRrCeC
����C���
���CRrCeC
����C��

�
�

�nrR

�nrn.

n

nrn.

nrR

�C�� 

�Fn �Pn �Rn n Rn Pn Fn

Figure 8. Rolling moment coefficient.

������������	
CeC
����C���
������������	
CeC
����C��
������������	
CeC
����C�����
���CRrCeC
����C���
���CRrCeC
����C��

�
�

�nrR

�nrn0.

�nrn.

�nrnP.

n

nrnP.

nrn.

nrn0.

�C� !

�Fn �Pn �Rn n Rn Pn Fn

Figure 9. Yawing moment coefficient.

propellers rotating clockwise and 23 percent with the
counter-rotating propellers. The reasons are higher
dynamic pressure on the vertical tail unit and the side
force component at the propeller discs created as a
result of sideslip.

The absolut value of derivative of the yawing mo-
ment with respect to the sideslip angle decreased about
6 percent. This can be caused by the interaction of
the propeller slipstream with the vertical tail unit.
This effect is more pronounced with increased sideslip
angle.

6.5. Influence of the type of rotation
of the propellers

As resulted from the previous analysis, the type of
rotation of the propellers is not negligible, but its
significance is moderate. Nevertheless, the differences
between the propellers rotating in the identical senses
and the counter-rotating propellers are registered in
the all studied relations. Probably the most impor-
tant from the point of view of the flying qualities
is the difference in the static longitudinal stability
where the counter-rotating propellers manifested even
more destabilizing effect than the propellers rotat-
ing in the identical senses. On the contrarry, the
counter-rotating propellers naturally do not cause the
aerodynamic asymmetries at the zero sideslip angle,
they are registered mainly at the roll moment with
the propellers rotating in the identical senses.

7. Discussion
The wind tunnel testing enabled estimation of the
influence of propellers positioned at the rear part
of the airplane on the principal aerodynamic and
stability characteristics of an airplane. In spite of
the position of the propellers at the afterbody of the
fuselage and thus limited influence on the wing, the
effect on longitudinal and lateral stability is significant
as the tailplanes even at T-configuration are evidently
affected to high extent.

List of symbols
b wingspan [m]
CL lift coefficient [–]
CL0 lift coefficient at α = 0 [–]
Cl rolling moment coefficient [–]
Cn pitching moment coefficient [–]
CQ torque coefficient related to %n2d5 [–]
CT thrust coefficient related to %n2d4 [–]
d propeller diameter [m]
J propeller advance ratio [–]
n propeller revolutions per second [s−1]
Q lift coefficient [Nm]
Qc torque coefficient related to 1

2%V
2Sb [–]

S aeroplane wing area [m2]
T propeller axial thrust [N]
CL thrust coefficient related to 1

2%V
2Sb [Tc]

V airspeed [ms−1]

α angle of attack [◦]
β sideslip angle [◦]
% air density [kgm3]

F S full scale
M model
CRP counter rotating propellers

References
[1] B. H. Luftschraubenstrahl und Längsstabilität.
Luftfahrtforschung, Vol. 11, p. 202 - 206,München and
Berlin 1935, 1935.

6

Figure 8. Rolling moment coefficient.

surprisingly strongly depends on the sense of rotation
of the propeller.

With the propeller blades moving from-up-to-down
in the proximity of the vertical tailplane (i.e., clockwise
turning on the left engine), the result is of a similar
nature as in the case of the conventional configura-
tion: the resulting yawing moment is approximately
1.25 higher than the product of the engine thrust and
its arm. With the opposite sense of rotation (i.e.,
counter-clockwise on the left engine), the yawing mo-
ment diminish to nearly zero, i.e., the aerodynamic
interference practically wipes out the moment created
by the engine thrust multiplied by its arm. It seems
to be a significant finding. However, with possible but
in practice probably limited impact. It implies that

4



vol. 57 no. 1/2017 An Airplane with Unconventionally Placed Propeller Power Units

������������	
CeC
����C���
������������	
CeC
����C��
������������	
CeC
����C�����
���CRrCeC
����C���
���CRrCeC
����C��

�
�

�nrR

�nrn0.

�nrn.

�nrnP.

n

nrnP.

nrn.

nrn0.

�C� !

�Fn �Pn �Rn n Rn Pn Fn

Figure 9. Yawing moment coefficient.

the desirable reduction of the vertical tailplane and
rudder could be possible but the real exploitation of
it would require the opposite senses of rotation of the
engines and thus two different versions of the engine
with different gearboxes.

From the point of view of the flow physics, it indi-
cates a strong interaction between the propeller and
the vertical tailplane and (maybe) the wing wake but
the exact nature of it remains to be clarified in detail.
Set of flow visualizations on the rear part of the fuse-
lage and on the vertical tailplane were performed but
without registering any significant difference.

6. Discussion
6.1. The influence of propellers on lift
A detectable difference is observed between the two
cases of the propeller rotation. The slope of the both
lift curves is almost identical, but CL0 for the counter-
rotating propellers is slightly lower, 4CL0 ≈ −0.02.
The explanation is probably in the flow over the
horizontal tailplane, as its right side was influenced
mainly by the counterclockwise rotating propeller
which rather decreases the angle of attack. In general,
the position of the propeller above and under the hor-
izontal surface, does not significantly change slope of
the lift curve.
The influence of the propellers placed on the wing

(REF. 1) is more significant. The increment 4CL0 ≈
0.1 is much higher than in the case of the non conven-
tional configuration. Higher increment of the lift coef-
ficient is due to the fact that the propeller slipstream
increases the local velocity around small portion of
the wing behind the propeller. The explanation for
the higher lift curve slope of the conventional configu-
ration can also be found in this phenomenon.

6.2. The influence of propellers
on static longitudinal stability
of an airplane without horizontal
tail surface

The direct effect of the thrust is removed from the
pitching moment characteristics by the positioning
the centre of gravity in the thrust line. The reference
points have identical longitudinal distance relative to
the mean aerodynamic cord for all tested configura-
tion. It is evident that the presence of the power units
has the stabilizing effect. The neutral point moves
backward by approximately 8 percent of the mean
aerodynamic cord for unconventional configuration
and by approximately 1 percent for the REF. 1 one.
The conventional configuration has the nose down
pitching moment. The explanation is that the in-
creased velocity over the part of the wing magnify the
wing pitchig moment. The significant effect of the
power units on the static stability of the unconven-
tional configuration can be explained as a stabilizing
effect of the propeller normal force. The pitching
moment of the unconventional configuration differs
around zero angle of attack where the propeller nor-
mal force supposed to be zero it can be resumed that
this nose-up pitchig moment has to be product of
changes in flowfield near pylons of the nacelle.

6.3. The influence of propellers
on static longitudinal stability
of a whole airplane

The influence of the rotating propellers on the hori-
zontal tailplane is pronounced as a longitudinal desta-
bilization of the airplane. The neutral point moved
forward by approximately 5 percent of the mean aero-
dynamic chord with the propellers rotating in the
identical senses, and by approximately 1 percent with
the counter-rotating propellers. With respect to the
fact that the propellers have an opposite influence
than in the case of the aircraft without the horizontal
taill, it seems possible to deduce that there is a very
significant influence of the propellers on the horizontal
tail, regardless the geometrical fact that the horizontal
tailplane is positioned high above the propellers and
only slightly behind the plane of the propeller discs.
The propellers create such changes in the flowfield
that it consequently led to the decreasing of the angle
of attack of the horizontal tailplane and thus to the
diminution of its lift (with respect to the convention
that positive lift was directed “upwards”). This influ-
ence is even more pronounced for the counter-rotating
propellers.
The almost constant nose-up pitching moment is

produced by the increased velocity under the hori-
zontal tail surface. A simillar phenomenon was also
reported in reference [16]. In that study, the aircraft
with the power units placed above the horizontal tail
surface was tested in the wind tunnel. This configura-
tion is marked as REF. 2 in Figure 7. and it can be
observed that the power units have stabilizing effect

5



J. Červinka, R. Kulhánek, Z. Pátek Acta Polytechnica

and add nose-down pitching moment. The neutral
point moves backward by approximately 3 percent of
the mean aerodynamic chord.

The rotating propellers of the conventional configu-
ration have adverse effect on the longitudinal static
stability. The neutral point moved forward by approx-
imately 12 percent of the mean aerodynamic chord.
It can be seen that the power effect change the static
margin without tail minimally so it can be deduced
that the propeller slipsteam changes the downwash
behind the wing and the horizontal stabilizer less
effectively.

6.4. The influence of propellers
on static lateral-directional
stability

6.4.1. Roll
The rotation of the propellers increases the “lateral sta-
bility”, i.e., increases the absolute value of the deriva-
tive of the rolling moment with respect to the sideslip
angle. The increase is approximately 16 percent with
both propellers rotating clockwise and 12 percent with
counter-rotating propellers. The probable reason is
the difference between the force components at the
left and the right propellers discs created as a result
of combination of the angle of attack and the sideslip
angle. This phenomenon is slightly suppressed by the
counter-rotating propellers. The reaction torque mo-
ment of the clockwise rotating propellers also causes
the negative rolling moment at the zero sideslip angle.
The moment is relatively high as its value corresponds
to the sideslip of 4 degrees.

The placement of the propeller on aircraft wing has
a negligible effect on the lateral stability. The shift of
the rolling moment coefficient at the zero sideslip angle
is caused by a wind tunnel airstream misalignment
according to reference [15].

6.4.2. Yaw
The influence of the propellers on the derivative of
the yawing moment with respect to the sideslip angle
is also highly pronounced, and the propeller opera-
tion significantly increases its value also in this case.
The increase is approximately 17 percent with the
propellers rotating clockwise and 23 percent with the
counter-rotating propellers. The reasons are higher
dynamic pressure on the vertical tail unit and the side
force component at the propeller discs created as a
result of sideslip.
The absolute value of the derivative of the yawing

moment with respect to the sideslip angle decreased by
about 6 percent. This can be caused by the interaction
of the propeller slipstream with the vertical tail unit.
This effect is more pronounced with the increased
sideslip angle.

6.5. The influence of the type
of rotation of the propellers

As resulted from the previous analysis, the type of
the rotation of the propellers is not negligible, but its
significance is moderate. Nevertheless, the differences
between the propellers rotating in the identical senses
and the counter-rotating propellers are registered in
all of the studied relations. Probably the most impor-
tant from the point of view of the flying qualities is
the difference in the static longitudinal stability where
the counter-rotating propellers manifested even more
destabilizing effect than the propellers rotating in the
identical senses. On the contrary, the counter-rotating
propellers do not naturally cause the aerodynamic
asymmetries at the zero sideslip angle, they are regis-
tered mainly at the roll moment with the propellers
rotating in the identical senses.

7. Summary
The wind tunnel testing enabled estimation of the
influence of propellers positioned at the rear part
of the airplane on the principal aerodynamic and
stability characteristics of an airplane. In spite of
the position of the propellers at the afterbody of the
fuselage and thus limited influence on the wing, the
effect on longitudinal and lateral stability is significant
as the tailplanes even at T-configuration are evidently
affected to a high extent.

List of symbols
b wingspan [m]
CL lift coefficient [–]
CL0 lift coefficient at α = 0 [–]
Cl rolling moment coefficient [–]
Cn pitching moment coefficient [–]
CQ torque coefficient related to %n2d5 [–]
CT thrust coefficient related to %n2d4 [–]
d propeller diameter [m]
J propeller advance ratio [–]
n propeller revolutions per second [s−1]
Q lift coefficient [N m]
Qc torque coefficient related to 1

2%V
2Sb [–]

S aeroplane wing area [m2]
T propeller axial thrust [N]
Tc thrust coefficient related to 1

2%V
2S [–]

V airspeed [m s−1]

α angle of attack [◦]
β sideslip angle [◦]
% air density [kg m3]

FS full scale
M model
CRP counter rotating propellers

References
[1] B. H. Luftschraubenstrahl und Längsstabilität.
Luftfahrtforschung, Vol. 11, p. 202 - 206,München and
Berlin 1935, 1935.

6



vol. 57 no. 1/2017 An Airplane with Unconventionally Placed Propeller Power Units

[2] S. J. Effect of Propeller Slipstream on Wing and Tail.
NACA TM 874, Washington, 1938.

[3] R. P. Aérodynamique expérimentale. Librairie
polytechnique Ch. Béranger, Paris and Lille, 1945.

[4] M. C. B. The Influence of Running Propellers on
Airplane Characteristics. Journal of the Aeronautical
Sciences, Vol. 7, no.3, pp. 85 - 103, 1940.

[5] S. J. H. A. Bell R. W. Some Aspects of the Effects of
Propeller Operation on the Static Longitudinal Stability
of an Airplane. Thesis. California Institute of
Technology, Pasadena, 1941.

[6] H. J. W. C. Kuhn R. E. Wind-Tunnel Investigation of
Effect of Propeller Slipstreams on Aerodynamic
Characteristics of a Wing Equipped with a
50-Percent-Chord Sliding flap and a 30-Percent-Chord
Slotted Flap. NACA TN 3918, Washigton, 1957.

[7] V. L. L. M. Propeller Wing Aerodynamic Interference.
Delft University of Technology, Delft, 2005.

[8] v. L. E. Miley S. J. Propeller Propulsion System
Integration, State of Technology Survey. NASA
CR-3982, 1985.

[9] E. M. E. Van Rooyen R. S. Assessment of propeller
influence on lateral-directional stability of multiengine
aircraft. Journal of Aircraft, Vol. 18, No. 5, pp. 364-371,
1981.

[10] S. R. Schroijen M.J.T. Propeller slipstream effects on
directional aircraft control with one engine inoperative.
AIAA-2007-1046, 2007.

[11] S. R. Schroijen M. J. T., Veldhuis L. L. M. Propeller
Slipstream Investigation Using the Fokker F27 Wind
Tunnel Modle with Flaps Deflected. ICAS Congress,
Anchorage, Congress Proceedings, pp. 360-1 – 360.14,
2008.

[12] D. S. G. Propeller. Airframe Aerodynamic Interference
on Twin Engine Aircraft. ICAS Congress, Harrogate,
Congress Proceedings, pp. 123.1 – 123.10, 2000.

[13] S. R. Schroijen M. J. T., Veldhuis L. L. M. Propeller
Empennage Interaction Effects onVertical Tail Design
of Multiengine Aircraft. Journal of Aircraft, Vol. 47,
No.4, pp. 1133-1140 DOI: 10.2514/1.46707, 2010.

[14] P. A. Barlow J. B., Rae W. H. Low-Speed Wind
Tunnel Testing, 3rd Edition. Wiley-Interscience, 1999.

[15] J. P. S. Muruin P. Fink, J. Charles C. Smith. A
wind-tunnel investigation of static longitudinal and
lateral characteristics of a full-scale mockup of a light
twing-engine airplane. National aeronautics and space
administration,Washington D.C., 1971.

[16] G. S. Rhodes. Low-speed wind-tunnel investigation of
the static stability and control characteristics of an
advanced turboprop configuration with the propellers
placed over the tail. North Carolina State University,
1990.

7


	Acta Polytechnica 57(1):1–7, 2017
	1 Introduction
	2 Review of current research
	3 Motivation
	4 Theory of similarity
	4.1 Propeller effects
	4.2 Model and testing device

	5 Results
	6 Discussion
	6.1 The influence of propellers on lift
	6.2 The influence of propellers on static longitudinal stability of an airplane without horizontal tail surface
	6.3 The influence of propellers on static longitudinal stability of a whole airplane
	6.4 The influence of propellers on static lateral-directional stability
	6.4.1 Roll
	6.4.2 Yaw

	6.5 The influence of the type of rotation of the propellers

	7 Summary
	List of symbols
	References