Comparison of Wing-Propeller Interaction in Tractor and Pusher Configuration

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Article
Comparison of wing–propeller interaction
in tractor and pusher configuration
Kwanchai Chinwicharnam and Chinnapat Thipyopas
Abstract
This research compared a tractor and a pusher configuration for a tilt-body vertical take-off and landing micro air vehicle
using an experiment in a subsonic wind tunnel. All tests were conducted in the range 6–10 m/s and 6000–8000 RPM of
the freestream and the propeller rotation, respectively. The wing model was a rectangular platform with an NACA 0012
airfoil and AR¼ 1. The incidence angles varied within the range 0�–90� to cover flight configuration from cruise to hover
and vice versa. Basically, the downstream of the propeller is stronger than the upstream. Thus the wing submerses in the
propeller’s downstream, which is the tractor configuration, and has an advantage over the other configuration by
increasing the freestream velocity and decreasing the angle of attack. The results of the experiment found that the
wing aerodynamics of the tractor were improved by the prop-wash effect with increases of about 1–1.13 times in the
wing lift curve slope and about 0.9–1.12 times in the factor K of the drag polar curve. However, in the case of the pusher,
the change was not significant. The stall angle, the maximum lift coefficient, and the drag coefficient at zero angle of the
wing all increased in both the tractor and the pusher configurations due to the prop-wash effect. Moreover, after
experiencing the prop-wash effect, the aerodynamic center of the tractor wing was almost at the same point.
Keywords
Micro Air Vehicle, Prop-wash Effect, Wing-Propeller Interaction
Date received: 19 September 2015; accepted: 5 February 2016
Introduction
Nowadays, many configurations of tilt-body micro air
vehicles (MAVs) have been developed, for example,
fixed wing and flapping wing. The fixed wing was the
focus of this research with the propeller’s position being
the specific area of study. Normally, there are two main
types of propeller position; where the propeller is
mounted at the wing leading edge and is known as a
‘‘tractor’’ and where the propeller is mounted at the
wing tailing edge, which is known as a ‘‘pusher.’’ The
wing aerodynamic characteristics of each are different
and their force and moment parameters were compared
in this study. Moreover, the interaction between the
wing and propeller in the type of pusher configuration
was studied in this research. Tractor configuration has
been formerly studied by Chinwicharnam et al.1
There are several MAV tractor configurations such
as Mini-Vertigo and MAVion shown in Figure 1(a) and
(b), respectively. The Mini-Vertigo MAV, which was
developed by Randall and Shkarayev2,3 and Bataille,4
is a coaxial propeller mounted at the wing leading edge.
These studies were performed in a subsonic wind
tunnel, and the results showed that the slipstream
flow influences the stall delay, lift enhancement and
drag and can increase the aerodynamic efficiency. The
MAVion from Supaero with two propellers was
designed by Itasse.5 The propeller’s dimension of the
MAVion covers almost the entire wing span, which
consequently improves the wing aerodynamic charac-
teristics due to the propeller downstream flowing
around the wing. Another type of research of the
wing and propeller interaction in the tractor configur-
ation was studied by Deng et al.6 using both experimen-
tal and numerical methods. They found that the
slipstream has a significant influence on the pressure
distribution on the wing surface, as well as investigating
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Department of Aerospace Engineering, Faculty of Engineering, Kasetsart
University, Bangkok, Thailand
Corresponding author:
Chinnapat Thipyopas, Department of Aerospace Engineering, Faculty of
Engineering, Kasetsart University, Bangkok 10900, Thailand.
Email: fengcpt@ku.ac.th
International Journal of Micro Air
Vehicles
January-March 2016: 3–20
! The Author(s) 2016
Reprints and permissions:
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DOI: 10.1177/1756829316638206
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and explaining the pattern of the wing-tip vortex at
different angles of attack with a rotary propeller.
Besides the tractor configuration, there is a new con-
ceptual design for a disk-wing aircraft shown in
Figure 1(c) which has been recently reported by
Ageev.7 This aircraft was designed using a slot in the
middle of the wing for a propeller in order to take
advantage of both the propeller upstream and the pro-
peller downstream. His results showed the good stall
characteristics of this concept, a low lift-to-drag ratio
and a sophisticated flow pattern. However, this config-
uration has only been reported in a few investigations.
The pusher configuration is not as well known as the
tractor configuration. Work was carried out by Choi
and Ahn8 using a commercial computational fluid
dynamics tool, FLUENT. They found that the propel-
ler effect retarded the flow separation on the upper sur-
face by 4� and it promoted the reattachment of the
separated flow, which contributed to increasing the
lift and the pitching-up moment on the vehicle, com-
pared with the wing without a propeller. The lift-to-
drag ratio was observed to be slightly lowered by
using a propeller, contrary to the commonly known
benefits of suppressed separation.
The propeller’s position is very important for the
improvement of wing aerodynamic characteristics as
studied by Catalano,9 Hrishikeshavan,10 Shkarayev,11
and Veldhuis12 for a full scale aircraft; the position of
the propeller has an influence on the wing boundary
layer characteristics such as laminar flow extension
and transition, laminar separation bubbles, and
reattachment and turbulent separation. Additionally,
the propeller slipstream produced a modified flow
over the wing where the kinetic energy increased, the
Reynolds number at wing surface increased and the
separation behavior changed. Therefore, the interaction
between the wing and propeller in a comparison of the
tractor and pusher configurations was investigated in
the current research.
In this study, the difference between the aero-
dynamic characteristics of the tractor and pusher
MAV configurations was investigated using six types
of models: the wing without and with propeller in
pusher and tractor configurations; a separated wing
and propeller in both the tractor and pusher; and the
last model involved propeller testing which can be seen
in more detail later in this paper. Testing measured the
aerodynamic forces and the moment of the models
using very accurate facilities and the methodology of
a wind tunnel experiment as suggested by Pope.13
Furthermore, all the models were tested to see the
effect of propeller wash on the wing aerodynamics
during transition flight. Moreover, the wing downwash
effect over the propeller, which several researches had
neglected, was considered in this paper.
Model test
The first campaign has already been completed using
the SabRe wind tunnel at Supaero, Toulouse, France.
The model test was a tractor configuration and the case
study was published in the literature.1 The current cam-
paign was performed using both the tractor configur-
ation and the pusher configuration in order to compare
a tractor and a pusher wing. The specifications of the
current model are shown in Table 1 and Figure 2(a) and
(b), which are similar to the previous model, but they
were built using a different 3D printer machine.
The wing model is a symmetrical airfoil that has the
wing lift at zero angle of attack and the aerodynamic
center is at about 25% of a wing chord.The tractor has
the propeller located far from the wing leading edge at
0.042m and also the pusher has the propeller located
far from the trailing edge at 0.042m. The wing surface
was made quite smooth using some sandpaper and by
painting. These processes were delicately undertaken
because of concerns about affecting the wing shape.
Experimental setup
A subsonic wind tunnel at Kasetsart University (KU),
Bangkok, Thailand was used in this experiment as
Figure 1. Current micro air vehicles: (a) Mini-Vertigo, (b) MAVion, and (c) Disk-wing aircraft.
4 International Journal of Micro Air Vehicles 8(1)
shown in Figure 3. The wind tunnel is a closed loop
and generates an airspeed in the range 6–10m/s. The
experiments were carried out in the square cross-section
which has dimensions of 1m� 1m� 3m (width�
height� length) with a contraction ratio of 4.0. The
fan speed was controlled by the container control
panels. The freestream velocity was recorded using
NI9215 hardware consisting of a National Instrument
Data Acquisition system (NI-DAQ) controlled by the
Labview software. The model was set in the middle of
the test section and was connected to a test bench which
contained a new, three-components, aerodynamic force
balance. The force balance was mounted with a manual
rotation system for increasing/decreasing the incidence
angle. The balance shown in Figure 4 was designed to
measure the lift, drag, and pitching moment simultan-
eously. Three load cells were installed on the balance
and it was connected to the NI9237 for sample record-
ing at 10 kHz. All load cells were calibrated using some
standard weights.
The installation scheme of the test bench mechanism
at the testing section is shown in Figure 5(a). The level
adjustment was carefully checked parallel to the wing
chord line and the freestream direction. Six experiments
were designed in this study as shown in Figure 5(b)–(g):
propeller test (PT), wing test (WT), mounted propeller
on wing model of the tractor/pusher test (MPWT/
MPWP), and separated propeller from wing model in
configurations of the tractor/pusher (SPWT/SPWP),
consecutively.
Test descriptions data accuracy
The wing (WT) model was tested and data were rec-
orded on the lift force, drag force, and pitching moment
as illustrated in Figure 6(a)–(c). The results recorded at
Supaero were used for comparison to investigate data
accuracy. Both the wind tunnel tests produced the same
aerodynamic behavior of the forces and moment for
various angles of attack. The lift coefficient at
Supaero was a little smaller than for the results at KU
but was not great taking into account the error bars.
Moreover, the stall of both was recorded at two angles
of 25� and 45�, and the curve of the drag force and
pitching moment coincided well with the results from
Supaero. The aerodynamic forces and moments that
were plotted with various Reynolds numbers from
129,000 to 300,000 based on the wing chord showed
that the results of the forces and moment were the
same curve by changing the angle of attack, e.g., the
lift curve slope, stall angle, CD0, and pitching-up or -
down angles. It can be said that there is small effect of
the Reynolds number for the low aspect ratio wing.
The aerodynamic characteristics of an isolated pro-
peller alone (PT) were recorded in the dynamic test
which considered the freestream at 10 and 6m/s, and
the propeller speed at 4000–6000 RPM as shown in
Figure 7(a) and (b). The thrust force was recorded at
various angles of attack from 0� to 90� in order to
observe the propeller aerodynamic behavior. It was
found that the thrust force increases as both the pro-
peller speed and the angle of attack increase. This can
be explained by the angles of attack increasing while the
Figure 2. Models set up in the wind tunnel: (a) tractor and (b) pusher.
Table 1. Model information.
Wing Information Value
Airfoil NACA 0012
Wing chord 0.3 m
Wing Span 0.3 m
Wing area 0.09 m2
Wing platform Rectangular
Material PLA (Polylactide)
Motor Type Brushless
Brand ALBATROSS 2215–1700 KV
Weight 70 g
Blade Type Garupner super nylon
Size 8� 600
Blade 2
Chinwicharnam and Thipyopas 5
freestream velocity of the propeller in the axial direc-
tion or the axial velocity is reduced. Note that the
behavior of a propeller at 90� with airspeed is like the
propeller at 0� without airspeed due to the fact
that the axial velocity of a propeller at 90� with airspeed
is equal to zero. The thrust coefficient measured at
Supaero was compared in Figure 7(b) with a propeller
speed of 6000 and V¼ 6m/s. There was a small error
between the results of Supaero and KU that was con-
sidered acceptable.
The mathematical model of the propeller thrust coef-
ficient as a function of the advance ratio and angle of
attack was determined and is expressed in equation (1)
when V¼ 10m/s, and in equation (2) when V¼ 6m/s.
The advance ratio is relative to the freestream velocity,
propeller speed, and propeller diameter as shown in
Table 2.
CT ffi 5:6213J
2 � 8:1388Jþ 0:00004�2MAV þ 0:001�MAV
þ 2:846 ð1Þ
CT ffi0:0614J
�2:463þ0:00004�2MAVþ0:003�MAV þ0:6739
ð2Þ
Free body diagram of models
The free body diagram of the models, a wing, propeller,
tractor, and pusher, are shown in Figure 8(a)–(d),
respectively. The isolated wing generates forces of lift
(L), drag (D), and moment (M) which are a vector
operation by a normal force (N) and axial force (A).
A propeller usually creates thrust force (T), lateral force
(Np), and torque (Q). The propeller moment can be
considered to be zero at the center of the propeller.
Furthermore, the propeller generates an induced vel-
ocity (w) in a downstream tube. Likewise, the tractor
and pusher configurations have the component of the
forces and moment as the combination of the wing and
the propeller which has been previously mentioned.
This research considered in particular the relation-
ships of the freestream velocity and the propeller rota-
tion in terms of the advance ratio which are shown in
Table 2. The formula equations for the aerodynamic
coefficients, Reynolds number, and advance ratio in
this paper can be calculated as
CL ¼
L
1
2�V
2S
, CD ¼
D
1
2�V
2S
, CM ¼
L
1
2�V
2Sc
,
CX ¼
D
1
2�V
2S
, CT ¼
T
1
2�V
2S
, CNp ¼
Np
1
2�V
2S
,
Re ¼
�Vd
�
, J ¼
V
nd
Results
Tractor/pusher wing and wing comparison
Lift coefficient. The aerodynamic behavior of the lift
coefficient as a function of the full range of angle of
attack for the SPWT (Separated Propeller-Wing in
Tractor Configuration), SPWP (Separated Propeller-
Wing in Pusher Configuration), and WT configurations
is compared in Figure 9(a)–(d) with different advance
ratios from 0.225 to 0.5. The lift coefficient of all wings
clearly increased as the angles of attack increased and it
increased until the stall angle. Then after stalling, it
slightly declined due to the high separation the adverse
Figure 3. Subsonic wind tunnel at Kasetsart University with
the experiment facilities.
Figure 4. Three-components force balance.
6 International Journal of Micro Air Vehicles 8(1)
Figure 5. Experiment setup of (a) components of the test bench and (b)–(g) six experiments.
-20 0 20 40 60 80 100
-0.2
0
0.2
0.4
0.6
0.8
αMAV (°)
C
L
Wing AR=1
Re 129000
Re 129000 Supaero
Re 215000
Re 300000
-20 0 20 40 60 80 100
-0.5
0
0.5
1
1.5
2
αMAV (°)
C
D
Wing AR=1
Re 129000
Re 129000 Supaero
Re 215000
Re 300000
-20 0 20 40 60 80 100
-0.1
0
0.1
0.2
0.3
0.4
αMAV (°)
C
M
(0
.2
5
c)
Wing AR=1
Re 129000
Re 129000 Supaero
Re 215000
Re 300000
Pitching down
Pitching up 
(a) (b)
(c)
Figure 6. Wing aerodynamic characteristics of forces and moment versus �MAV .
Chinwicharnam and Thipyopas 7
pressure gradient presented to the flow. Notably, the
stall angle of the tractor/pusher wing was delayed
from 20� to a range between 45� and 55� by the effect
of prop-wash. Furthermore, the prop-wash effect
increased the maximum lift coefficient (CLmax) and
the lift–curve slope (CLa) in both the tractor/pusherwings.
The results shown in Figure 9(a)–(d) illustrate that
the performance of the tractor wing is clearly better
than for the pusher wing profile. The performance of
both the tractor and pusher wing profiles is character-
ized by the lift coefficient. The results showed that the
CLmax of the tractor wing increased from the CLmax of
the wing alone in the range 91–232%, while the CLmax
of the pusher wing increased only 76–104% for the
wing alone. This was due to the fact that the wing of
the tractor benefits from the increasing airspeed ema-
nating from the propeller downstream (Vþw), while
the wing of the pusher benefits from the propeller
upstream. It should be noted that the propeller down-
stream had a higher flow energy instance (i.e., a turbu-
lent and complex flow) than the propeller upstream.
Moreover, the wings will have an effective angle of
attack as mentioned in the study by Chinwicharnam
et al.1 It seems the tractor wing has a less effective
angle (awing) than the wing pusher and has a new,
higher airspeed (V0). The values for CLmax for all
wings are shown in Table 3.
When considering the difference between the CLmax
of the tractor wing and the pusher wing at J¼ 0.225,
0.3, 0.375, and 0.5, the CLmax of tractor wing was
greater by around 128%, 88%, 39%, and 15%, respect-
ively, as shown in Figure 9(a)–(d). The difference in
CLmax reduced when the advance ratio increased
because the lift coefficient is in inverse proportion to
the freestream (V) and the wing lift coefficient of the
pusher is quite independent of the airspeed or the
advance ratio.
Apart from the lift–curve slope (CLa) of the wing
alone, the angle of attack from 0� to 15�, was constant
at 0.039 for each advance ratio. The CLa values of the
tractor wing were 0.062, 0.061, 0.047, and 0.044,
respectively, for advance ratios of J¼ 0.225, 0.3,
0.375, and 0.5, and were 0.041, 0.040, 0.040, and
0.039, respectively, for the pusher wing as shown in
Table 3. In general, the CLa of the tractor wing was
higher than for the pusher wing at every advance
ratio due to the fact that the wing of the tractor has a
propeller boost airspeed that promotes an increase in
the lift force.
The advance ratio was increased by decreasing the
propeller rotational speed, and this is shown in the
comparison between Figure 9(a) and (b), and between
Figure 9(c) and (d). It was found that the CLa of both
the tractor/pusher wings was reduced as illustrated in
Table 3 because the induced velocity of the propeller
(w) dropped due to the decreasing slipstream resulting
velocity (VR). The slipstream resulting velocity of the
tractor wing was plotted with model angles at various
advance ratios as shown in Figure 10, according to cal-
culation using the McCormick14 equation. Note that
the propeller upstream of the pusher wing did not
experience the induced airspeed, but its trend of
Table 2. Advance ratio equivalences.
V(m/s) Re RPM J
6 12,9000 6000 0.300
6 8000 0.225
10 215,000 6000 0.500
10 8000 0.375
0 20 40 60 80 100
-0.5
0
0.5
1
1.5
αMAV (°)
C
T
Propeller V = 10 m/s
N 4000
N 6000
N 8000
0 20 40 60 80 100
0
0.5
1
1.5
2
2.5
3
αMAV (°)
C
T
Propeller V = 6 m/s
N 6000
N 6000 Supaero
(a) (b)
Figure 7. Propeller aerodynamic characteristics of forces and moments versus �.
8 International Journal of Micro Air Vehicles 8(1)
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Figure 8. Forces and moments diagrams.
-20 0 20 40 60 80 100
-1
0
1
2
3
4
αMAV (°)
C
L
w
+ Δ
C
Lp
ro
p
→
w
in
g
Wing prop-wash effect, J = 0.225, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
-1
0
1
2
3
4
αMAV (°)
C
L
w
+ Δ
C
Lp
ro
p
→
w
in
g
Wing prop-wash effect, J = 0.3, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
-1
0
1
2
3
4
αMAV (°)
C
Lw
+ Δ
C
L
pr
o
p
→
w
in
g
Wing prop-wash effect, J = 0.375, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
-1
0
1
2
3
4
αMAV (°)
C
Lw
+ Δ
C
L
pr
o
p
→
w
in
g
Wing prop-wash effect, J = 0.5, AR = 1
Tractor
Pusher
Wing
232% 
104% 
117%
89%
129% 
91% 91%76%
(a) (b)
(c) (d)
Figure 9. Comparison of lift coefficient of the wing prop-off and prop-wash effect versus �MAV .
Chinwicharnam and Thipyopas 9
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slipstream resulting velocity versus model angles should
be similar to that of the tractor wing.
Drag coefficient. The aerodynamic behavior of the three
particular models is explained through a comparison of
the drag coefficient for advance ratios between 0.225
and 0.5, as illustrated in Figure 11(a)–(d). Even if the
prop-wash can enhance the wing lift and even extend
the stall, it will simultaneously induce drag force in
both the tractor and pusher configurations. The drag
coefficient of the wing with the propeller increases
because the prop-wash will generate a complex flow
with high turbulence and also increase the freestream
velocity across the wings and the propeller. Indeed, the
increasing freestream velocity will influence the wing tip
vortex. Because the wing model used in this study is a
low aspect ratio, the drag induced from the wing alone
model is significantly contributed to by the tip vortex.
The wing tip vortex increases as the angle of attack is
increased. It therefore can be said that the drag of the
wing increases as the angle of attack increases. For the
tractor and pusher configurations, the drag coefficient
increased until it reached the stall angle after which it
then decreased. The maximum value of CD depends
upon the advance ratio. Table 4 shows the maximum
CD for the pusher and tractor configurations for four
different advance ratios and their corresponding angle
of attack.
It can be seen from the results accumulated in
Table 4 that for both the pusher and tractor configur-
ations, the CDmax decreases as the advance ratio
increases. Figures 11(a) and 7(b), respectively, represent
the drag coefficient results for J¼ 0.225 and J¼ 0.3 and
show that the drag coefficient of the tractor wing is
always higher than for the pusher wing because the
tractor wing submerges in the propeller downstream.
Ideally, the propeller downstream generates a turbulent
flow to the wing where this turbulent flow is also stron-
ger than the wing submerged in the propeller upstream.
Therefore, the tractor wing increases the parasite drag,
defined as the summation of skin friction and pressure
drag. For advance ratios of 0.375 and 0.5 shown in
Figure 11(c) and (d) which correspond to a velocity
of 10m/s, the drag coefficient of the tractor wing is a
little lower than the pusher wing profile. This might be
caused by the decrease in the induced velocity of the
propeller. When the propeller induced velocity (w)
decreased due to the increasing airspeed (V¼ 10m/s),
the new angle of attack (aw) of the wing due to the
combination of airspeed and propeller-induced
velocity (Vþw) must be lower than the tractor wing
at V¼ 6m/s. The minimum drag coefficient of all
models was found at 0� and the factor K of the drag
polar curve which is used to calculate CD of wing in
equation (3)) is shown in Table 5.
CD ¼ CD0 þ KC
2
L ð3Þ
Aerodynamic efficiency. The lift-to-drag ratio, which can
be represented as the efficiency of MAVs, was plotted
by changing the advance ratios from 0.225 to 0.5 for
various angles of attack as shown in Figure 12(a)–(d).
The results of all models have a general trend which
increased greatly over a small range of angle (0�–15�)
Table 3. CLa (0–15�) and CLmax for wing, tractor, and pusher configurations with their corresponding angle of attack.
J
Wing Tractor Pusher
CLmax astall CLa(0–15�) CLmax astall CLa(0–15�) CLmax astall CLa(0–15�)
0.225 0.876 (Re 129,000) 25� 0.039 2.908 55� 0.062 1.786 50� 0.041
0.300 2.430 50� 0.061 1.657 45� 0.040
0.375 0.855 (Re 215,000) 25� 0.039 1.960 50� 0.047 1.629 50� 0.040
0.500 1.634 45� 0.044 1.505 45� 0.039
-20 0 20 40 60 80 100
0.5
1
1.5
2
2.5
3
3.5
4
αMAV (°)
V
r/V
∞
D
prop
 = 0.2 m, 2 Blade
J = 0.225
J = 0.300
J = 0.375
J = 0.500
Figure 10. Comparisonof the propeller speed influence on the
slipstream resulting velocity and freestream velocity ratio of
tractor wing versus �MAV .
10 International Journal of Micro Air Vehicles 8(1)
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and then reached a maximum L/D ratio after which the
trend gradually reduced. The maximum L/D ratio of
the wing with the propeller in both tractor and pusher
configurations was lower than for the wing alone
because the prop-wash effect induced a drag force to
the wing. Considering the advance ratios of J¼ 0.225,
0.3, 0.375, and 0.5, the maximum L/D ratio for the
tractor wing decreased from the maximum L/D ratio
of wing without a propeller by 15%, 30%, 25%, and
30%, respectively, and also the maximum L/D ratio for
the pusher wing decreased 28% 35%, 41%, and 40%,
respectively, of the maximum L/D ratio of the wing
without a propeller. The trend of L/D at each advance
ratio can be divided into two zones—wing pre-stall and
wing post-stall. In the wing pre-stall zone, the L/D ratio
of the wing decreased when the propeller was
-20 0 20 40 60 80 100
0
1
2
3
4
αMAV (°)
C
D
w
+ Δ
C
D
pr
op
→
w
in
g
Wing prop-wash effect, J = 0.225, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
0
1
2
3
4
αMAV (°)
C
D
w
+ Δ
C
D
pr
op
→
w
in
g
Wing prop-wash effect, J = 0.3, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
0
1
2
3
4
αMAV (°)
C
D
w
+ Δ
C
D
pr
op
→
w
in
g
Wing prop-wash effect, J = 0.375, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
0
1
2
3
4
αMAV (°)
C
D
w
+ Δ
C
D
pr
op
→
w
in
g
Wing prop-wash effect, J = 0.5, AR = 1
Tractor
Pusher
Wing
(a) (b)
(c) (d)
Figure 11. Comparison of drag coefficient of the wing prop-off and prop-wash effect versus �MAV .
Table 4. Maximum CD for pusher and tractor configurations
and their corresponding angle of attack.
J
Wing Tractor Pusher
CD(max)
aCD
(max)
CD
(max)
aCD
(max)
CD
(max)
aCD
(max)
0.225 1.56 (Re 129,000) 90� 4.25 70� 2.8 65�
0.300 3.20 60� 2.5 60�
0.375 1.48 (Re 215,000) 90� 2.20 55� 2.25 60�
0.500 1.80 50� 1.8 60�
Table 5. Minimum CD and the factor K of the drag polar equa-
tion for pusher and tractor configurations.
J
Wing Tractor Pusher
CD0
K
(0�–20�) CD0
K
(0�–20�) CD0
K
(0�–20�)
0.225 0.014 (Re 129,000) 0.45 0.099 0.28 0.088 0.52
0.300 0.093 0.29 0.115 0.48
0.375 0.014 (Re 215,000) 0.45 0.091 0.30 0.102 0.44
0.500 0.070 0.39 0.101 0.44
Chinwicharnam and Thipyopas 11
attached and the L/D ratio of the pusher wing was the
lowest. In the wing post-stall zone, the tractor wing had
the highest aerodynamic efficiency due to the fact that
the prop-wash effect improves the flow around the trac-
tor wing, such as in a delayed stall, increasing the air-
speed and promoting flow reattachment. The highest
aerodynamic efficiency of the tractor wing is very
useful for the tilt-body MAV configuration because it
will save battery power during the flight and be an
advantage during a transition flight. The MAV can
easily tilt its body from horizontal flight to vertical
flight using a small amount of battery energy.
Moreover, it increases the performance of the MAV
at a very high incidence angle.
Table 6 shows the maximum L/D ratio for the wing,
tractor, and pusher configurations for four different
advance ratios and their corresponding angles of
attack. The maximum L/D ratio of the wing without
a propeller was at 10�, and it increased as the Reynolds
number increased. The maximum L/D ratio of the
-20 0 20 40 60 80 100
0
1
2
3
4
αMAV (°)
(L
/D
) w
in
g&
pr
o
p-
w
a
sh
Wing prop-wash effect, J = 0.225, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
0
1
2
3
4
αMAV (°)
(L
/D
) w
in
g&
pr
o
p-
w
a
sh
Wing prop-wash effect, J = 0.3, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
0
1
2
3
4
αMAV (°)
(L
/D
) w
in
g&
pr
o
p-
w
a
sh
Wing prop-wash effect, J = 0.375, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
0
1
2
3
4
αMAV (°)
(L
/D
) w
in
g&
pr
o
p-
w
a
sh
Wing prop-wash effect, J = 0.5, AR = 1
Tractor
Pusher
Wing
Wing pre-stall Wing pre-stall
Wing pre-stall Wing pre-stall
Wing post-stall Wing post-stall
Wing post-stall Wing post-stall
-15% -28% -30% -35%
-25% -41% -39% -40%
(a) (b)
(c) (d)
Figure 12. Comparison of aerodynamic efficiency of the wing prop-off and prop-wash effect versus �MAV .
Table 6. Maximum ratio (L/D)max for wing, tractor, and pusher configurations and their corresponding angles of attack.
J
Wing Tractor Pusher
(L/D)max a(L/D)max (L/D)max a(L/D)max (L/D)max a(L/D)max
0.225 3.50 (Re 129,000) 10� 2.97 10� 2.52 15�
0.300 2.47 15� 2.27 15�
0.375 4.16 (Re 215,000) 10� 3.14 15� 2.45 10�
0.500 2.55 15� 2.48 10�
12 International Journal of Micro Air Vehicles 8(1)
tractor wing decreased when the advance ratio was
increased by decreasing the RPM only; for example,
J¼ 0.225 to J¼ 0.3. The maximum L/D ratio of the
tractor wing was changed a small amount by the
advance ratio. It should be noted that both the tractor
and pusher wings had an angle of maximum L/D ratio
of around 10�–15� which is dependent on the
advance ratio.
Moment coefficient. A part of the wing moment behavior,
for example pitching up/down, is also important in the
design and development of MAVs. The pitching
moment of the isolated wing and the wing with propel-
ler were measured at 25% of the wing chord-wise for a
full range of angles of attack as shown in Figure 13(a)–(d).
All models generated a negative moment or pitching up
in the range of angle of attack from 0�–10� or 0�–15�,
depending on their advance ratio. Above this angle, the
pitch slope of all wings rose with a further increasing
angle of attack up to stalling. At an angle of 20�–40� in
every advance ratio, the positive moment of the tractor
wing was less than the wing alone, due to the fact that
the prop-wash effect improved the flow around the
tractor wing. For example, it decreased the angle of
attack, increased the airspeed, and delayed stalling.
Above about 40�, the pitching-up moment of the trac-
tor wing still increased and was higher than for the wing
alone. Increased pitching up is generated by the wing
lift, and this contributes to the prop-wash effect.
However, the pusher wing had the highest pitching up
and the lowest pitching down for every angle of attack
and every advance ratio. The moment of the tractor
wing was more stable than for the pusher wing at
every angle, although the pitching down of the tractor
wing was lower at a small angle of attack, but it was
just a small value.
According to the plot of CM for various angles of
attack, the slope of the moment coefficient (Cm,a (0–5�))
was found by using an angle from 0� to 5�, and the
aerodynamic center was calculated as a percentage of
the chord as shown in Table 7. The Cm,a(0–5�) of the
wing was reduced by increasing the Reynolds number,
while the Cm,a(0–5�) of the tractor was not very sensitive
to the various advance ratios. On other hand, the
Cm,a(0–5�) of the pusher increased by increasing
the advance ratio. The aerodynamic center of both
-20 0 20 40 60 80 100
-0.1
0
0.1
0.2
0.3
0.4
0.5
αMAV (°)
(C
M
w
+ Δ
C
M
p
ro
p
→
w
in
g
) 0
.2
5c
Wing prop-wash effect, J = 0.225, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
-0.1
0
0.1
0.2
0.3
0.4
0.5
αMAV (°)
(C
M
w
+ Δ
C
M
p
ro
p
→
w
in
g
) 0
.2
5c
Wing prop-wash effect, J = 0.3, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
-0.1
0
0.1
0.2
0.3
0.4
0.5
αMAV (°)
(C
M
w
+ Δ
C
M
p
ro
p
→
w
in
g
) 0
.2
5c
Wing prop-wash effect, J = 0.375, AR = 1
Tractor
Pusher
Wing
-20 0 20 40 60 80 100
-0.1
0
0.1
0.2
0.3
0.4
0.5
αMAV (°)
(C
M
w
+ Δ
C
M
p
ro
p
→
w
in
g
) 0
.2
5c
Wing prop-wash effect, J = 0.5, AR = 1
Tractor
Pusher
Wing
Pitching down
Pitching up 
Pitching down 
Pitching up 
Pitching up 
Pitching down 
Pitching up 
Pitching down
(a) (b)
(c) (d)
Figure 13. Comparison of pitching moment coefficient of the wing prop-off and prop-wash effectversus �MAV .
Chinwicharnam and Thipyopas 13
the isolated wing and the tractor was extended to 30%
of the chord by increasing the freestream, but in case of
the pusher, there was not much change.
Wing and prop-wash effect
Lift coefficient
The total lift coefficient of the pusher can be determined
using equation (4) which combines the lift of the wing,
the propeller, the effect of propeller wash
(DCLprop!wing), and the effect of wing wash
(DCLwing!prop). The propeller lift and wing-wash effects
are considered as shown in Figure 14(a) and (b). The
lift curve slope (CLa) of the total lift increased to 0.050
and 0.044 when the advance ratio was 0.375 and 0.5,
respectively. It should be noted that the CLa values are
calculated by using an angle range of 0� to 15�.The stall
angle of the wing prop-on (Total) is at the same point
as the wing with prop-wash effect. The propeller lift
force increased with increasing angle of attack due to
the decrease in the axial velocity of the propeller. When
the propeller lift force is considered, the maximum of
CLtotal at J¼ 0.375 increased 61% from the maximum
wing prop-wash while at J¼ 0.5, the maximum CLtotal
increased 35% from the maximum wing prop-wash.
CLtotal ¼ CLwing þ CLprop þ�CLprop!wing þ�CLwing!prop
ð4Þ
A comparison between the prop-wash
effect (DCLprop!wing) and the wing-wash effect
(DCLwing!prop) is shown in Figure 15(a) and (b).
At advance ratios of 0.375 and 0.5, the propeller
wash had a small effect in the range 0�–15�; the wing
has an effective angle which is not as high as the model
angle, and at the same time, as this wing has a low
aspect ratio, the lift curve is slight. Above an angle of
15�, the lift force increased with increasing angle of
attack until the stall angle. Then, the lift coefficient
gradually decreased for post-stall angles. A small
wing-wash effect was observed compared with the
prop-wash effect.
Total longitudinal force coefficient. The interaction between
the pusher wing and the propeller in terms of the drag
force coefficient and the total longitudinal force coeffi-
cient are shown in Figure 16(a) and (b). The negative
CD represents the thrust direction of models which can
be found in the propeller force and the wing prop-on. It
is clear that the curve of CD of wing prop-on shifted
down in quantify of the propeller CD. Therefore, it is
possible to derive equation (5) to explain this relation.
The CDa¼ 0 of the wing prop-wash effect was higher
Table 7. Cm,a (0–5�) and ac. for wing, tractor, and pusher con-
figurations (Boldface in Table 7 shows a change or move of ac).
J
Wing Tractor Pusher
Cm,a
(0–5�) ac. (%c) Cm,a (0–5�)
ac.
(%c)
Cm,a
(0–5�)
ac.
(%c)
0.225 �0.0010
(Re 129,000)
27.83 �0.0022 28.50 �0.0012 27.90
0.300 �0.0023 28.86 �0.0010 27.60
0.375 �0.0018
(Re 215,000)
30.07 �0.0024 30.15 �0.0008 27.14
0.500 �0.0023 30.28 �0.0007 26.87
Wing prop-off (C
⊗w ing
) Wing prop-on (C
⊗total
) Propeller (C
⊗prop
) Prop wash (C
⊗w ing
+ΔC⊗prop→w ing)
-20 0 20 40 60 80 100
-0.5
0
0.5
1
1.5
2
2.5
3
αMAV (°)
C
L
Pusher, J = 0.375, AR = 1
-20 0 20 40 60 80 100
-0.5
0
0.5
1
1.5
2
2.5
3
αMAV (°)
C
L
Pusher, J = 0.5, AR = 1
CLa =0.039 
CLa =0.040 CLa =0.050 
CLa =0.039
CLa =0.040CLa =0.044
91% 76%152% 111%
35%
61% 
(a) (b)
Figure 14. Wing prop-on/prop-off and prop-wash effect in terms of lift coefficient versus �MAV : (a) J¼ 0.375 and (b) J¼ 0.5.
14 International Journal of Micro Air Vehicles 8(1)
than the wing prop-off due to the propeller increasing
the freestream velocity and turbulent flow around the
pusher wing. The propeller had a constant effect on the
wing for the range 0�–20� which is the angle before
wing prop-off stall; it can be observed that the differ-
ence between the CD of the wing prop-off and the wing
prop-wash was constant in this angle range because the
effective angle of attack (aw) changed little when the
wing increased the angle of attack (aMAV) and it hap-
pened only at an angle before the stall of wing prop-off.
After an aMAV value of 20�, the wing prop-wash
strongly increased due to the complex flow by the
prop-wash effect. It should be noted that the propeller
can produce more thrust when the angle of attack is
increased due to the fact that the freestream velocity,
which is perpendicular to the propeller plane, is
decreased by the increasing propeller angle of attack.
CXtotal ¼ CDwing þ CDprop þ�CDprop!wing þ�CDwing!prop
ð5Þ
The drag coefficients of the prop-wash
effect (DCDprop!wing) and the wing-wash effect
(DCDwing!prop) of the pusher wing for various angles
of attack are shown in Figure 17(a) and (b). The pro-
peller wash had a small effect on the wing in the range
0�–20� and then it increased with increment in the angle
of attack. The drag force of the wing-wash effect was
less than the prop-wash effect as the lift force. However,
-20 0 20 40 60 80 100
-0.5
0
0.5
1
1.5
2
2.5
3
αMAV (°)
C
L
Pusher, J = 0.375, AR = 1
ΔCLprop→w ing
ΔCLw ing→prop
-20 0 20 40 60 80 100
-0.5
0
0.5
1
1.5
2
2.5
3
αMAV (°)
C
L
Pusher, J = 0.5, AR = 1
ΔCLprop→w ing
ΔCLw ing→prop
Pre-stall Post-stall Pre-stall Post-stall
(a) (b)
Figure 15. Prop-wash and wing-wash effect in terms of lift coefficient versus �MAV : (a) J¼ 0.375 and (b) J¼ 0.5.
Wing prop-off (C
⊗w ing
) Wing prop-on (C
⊗total
) Propeller (C
⊗prop
) Prop wash (C
⊗w ing
+ΔC⊗prop→w ing)
-20 0 20 40 60 80 100
-1
0
1
2
3
αMAV (°)
C
D
Pusher, J = 0.375, AR = 1
-20 0 20 40 60 80 100
-1
0
1
2
3
αMAV (°)
C
D
Pusher, J = 0.5, AR = 1
Drag
Thrust 
Drag
Thrust
(a) (b)
Figure 16. Wing prop-on/off and prop-wash effect in terms of drag coefficient versus �MAV : (a) J¼ 0.375 and (b) J¼ 0.5.
Chinwicharnam and Thipyopas 15
the results show that there was a minor effect of wing
wash at J¼ 0.5.
Pitching moment coefficient. The pitching moment was
measured at 25% of wing chord as shown in
Figure 18(a) and (b), with a negative value representing
pitching down and a positive value referring to pitching
up. The total pitching moment can be determined using
equation (6). The influence of CMprop was very slight
compared with CMwing for various angles of attack
due to the fact that there was only the CNp influence
on the propeller pitching moment. As mentioned in the
previous studies,1,15 the propeller at the incidence angle
generated the resultant propeller thrust (CT), which was
not applied at the center of the propeller due to the
asymmetric distribution of the thrust over the propeller
disk. However, the radius of the current propeller was
very small due to the fact that the total axial thrust does
not displace more than 45% from the center of the
propeller. Therefore, it is safe to assume that for this
type of propeller, the pitching moment which is pro-
duced by CTr can be neglected.
CMtotal¼CMwingþCMpropþ�CMprop!wingþ�CMwing!prop
ð6Þ
where CMprop ¼ CTrþ CNpx0:25c
-20 0 20 40 60 80 100
-1
0
1
2
3
αMAV (°)
C
D
Pusher, J = 0.375, AR = 1
ΔCDprop→w ing
ΔCDw ing→prop
-20 0 20 40 60 80 100
-1
0
1
2
3
αMAV (°)
C
D
Pusher, J = 0.5, AR = 1
ΔCDprop→w ing
ΔCDw ing→prop
(a) (b)
Figure 17. Prop-wash and wing-wash effect in terms of drag coefficient versus �MAV : (a) J¼ 0.375 and (b) J¼ 0.5.
Wing prop-off (C
⊗w ing
) Wing prop-on (C
⊗total
) Propeller (C
⊗prop
) Prop wash (C
⊗w ing
+ΔC⊗prop→w ing)
-20 0 20 40 60 80 100
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
αMAV (°)
C
M
(0
.2
5
c)
Pusher, J = 0.375, AR = 1
-20 0 20 40 60 80 100
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
αMAV (°)
C
M
(0
.2
5
c)
Pusher, J = 0.5, AR = 1
Pitching up
Pitching down
Pitching up 
Pitching down 
(a) (b)
Figure 18. Wing prop-on/prop-off and prop-wash effect in terms of pitching moment coefficient versus �MAV : (a) J¼ 0.375
and (b) J¼ 0.5.
16 International Journal of Micro Air Vehicles 8(1)
Comparison of the pitching moment coefficients of
the prop-wash effect (DCMprop!wing) and the wing-wash
effect (DCMwing!prop) are shown in Figure 19(a) and
(b). The wingwash affected the pitching-down
moment of the wing when J¼ 0.375 with quite a high
result as shown in the plot. However, it was small
compared with the pitching-up moment of the prop-
wash effect in both advance ratios. The maximum
CM(0.25c) of the prop-wash effect occurred at 60
� and
50�, when the advance ratio was 0.375 and 0.5,
respectively.
Total aerodynamic forces and moment of pusher
The mounted propeller on the wing model of the trac-
tor/pusher test (MPWT/MPWP) was tested by measur-
ing the lift force, drag force, and pitching moment as
shown in Figure 20(a)–(f). The total forces and the
moment are plotted to help users consider the capabil-
ity of these models. The results were also plotted with
the error bar from the experiment. The CLa values of
both the tractor and pusher tended to increase when the
advance ratio decreased, while the maximum CL and
stall angle increased as shown in Figure 20(a) and (b).
The CL of both tractor and pusher equaled zero, due to
the fact that the wing had a symmetrical airfoil NACA
0012 and the Np of the propeller can be ignored. The
longitudinal force of the tractor and pusher as shown in
Figure 20(c) and (d) combined normally with the thrust
and drag force. The tractor and pusher drag increased
with an increasing angle of attack. The thrust of the low
advance ratio was lower than the thrust of the high
advance ratio because of the reduction in airspeed.
Pitching-up or -down moment occurred with both the
tractor and pusher as shown in Figure 20(e) and (f).
The range of the pitching-down moment for the tractor
was longer than for the pusher being almost 35� while
the pusher was only 20�. The pitching-down moment at
aMAV¼ 0� of the pusher increased with a decrease in the
advance ratio and was higher than for the tractor
because the propeller lateral force (Np) of the
pusher was located at the wing tailing edge as shown
in Figure 8 and the length of x0.25c of the pusher was
more than for the tractor.
Conclusions
This research provides a comparison between the trac-
tor-wing and the pusher-wing configuration of a tilt-
body MAV using experimental data. Testing was
performed using a low Reynolds number following
the real-flight situation of MAVs at V¼ 6, 10m/s and
J¼ 0.225–0.5. The results were used to determine that
the aerodynamic performance of the tractor configur-
ation was better than for the pusher configuration, as
the stall angle, lift–curve slope, maximum lift coeffi-
cient, and aerodynamic efficiency of the tractor wing
were higher than for the pusher wing. Furthermore,
the zero-lift drag coefficient of the tractor wing was
lower than for the pusher wing. Thus, a tilt-body
MAV can obtain great advantage from the tractor
wing configuration; for example, a tractor wing
during transition flight has a very high angle of attack
and can generate a higher L/D ratio than a pusher
wing. This will be useful in terms of saving battery
power and increasing payloads.
The propeller improved the aerodynamic character-
istics in both the wing tractor and pusher by increasing
the lift and drag coefficient. It was noticed that the
propeller increased the airspeed and decreased the
angle of attack of the wing and helped the wing surface
to have a greater reattachment boundary layer which
extends the separation behavior and delays the wing-
stall angle. These results showed that the tractor/pusher
wing could take advantage from both the upstream and
downstream of the propeller.
-20 0 20 40 60 80 100
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
αMAV (°)
C
M
(0
.2
5
c)
Pusher, J = 0.375, AR = 1
ΔCMprop→w ing
ΔCMw ing→prop
-20 0 20 40 60 80 100
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
αMAV (°)
C
M
(0
.2
5
c)
Pusher, J = 0.5, AR = 1
ΔCMprop→w ing
ΔCMw ing→prop
Pitching up
Pitching down 
Pitching up
Pitching down
(a) (b)
Figure 19. Prop-wash and wing-wash effect in terms of pitching moment coefficient versus �MAV : (a) J¼ 0.375 and (b) J¼ 0.5.
Chinwicharnam and Thipyopas 17
Paulo
Realce
The aerodynamic total forces and moment of the
pusher configuration were derived so that they com-
bined the forces and moment of an isolated wing, an
isolated propeller, a prop-wash effect, and a wing-wash
effect. The prop-wash effect mainly increased the
aerodynamic performance of the wing, but the wing–
wash effect was just a small part of this interaction.
However, the wing-wash effect cannot be ignored as
also mentioned in previous study.1 The total lift and
drag coefficient, the maximum lift coefficient, the stall
-20 0 20 40 60 80 100
-1
0
1
2
3
4
5
6
αMAV (°)
C
L
T
ot
al
Wing prop-on (Tractor), AR=1, D=0.2
J = 0.225
J = 0.3
J = 0.375
J = 0.5
-20 0 20 40 60 80 100
-1
0
1
2
3
4
αMAV (°)
C
L
T
ot
al
Wing prop-on (Pusher), AR=1, D=0.2
J = 0.225
J = 0.3
J = 0.375
J = 0.5
-20 0 20 40 60 80 100
-3
-2
-1
0
1
2
3
4
αMAV (°)
C
D
T
ot
al
Wing prop-on (Tractor), AR=1, D=0.2
J = 0.225
J = 0.3
J = 0.375
J = 0.5
-20 0 20 40 60 80 100
-3
-2
-1
0
1
2
3
αMAV (°)
C
D
T
ot
al
Wing prop-on (Pusher), AR=1, D=0.2
J = 0.225
J = 0.3
J = 0.375
J = 0.5
-20 0 20 40 60 80 100
-0.1
0
0.1
0.2
0.3
0.4
αMAV (°)
C
M
(0
.2
5c
)T
ot
a
l
Wing prop-on (Tractor), AR=1, D=0.2
J = 0.225
J = 0.3
J = 0.375
J = 0.5
-20 0 20 40 60 80 100
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
αMAV (°)
C
M
(0
.2
5c
)T
ot
a
l
Wing prop-on (Pusher), AR=1, D=0.2
J = 0.225
J = 0.3
J = 0.375
J = 0.5
Drag
Thrust 
Drag
Thrust
Pitching up
Pitching down 
Pitching up
Pitching down
(a) (b)
(c) (d)
(e) (f)
Figure 20. Aerodynamic characteristics of tractor and pusher in various advance ratios: (a), (b) lift coefficient; (c),
(d) drag coefficient; and (e), (f) pitching moment coefficient.
18 International Journal of Micro Air Vehicles 8(1)
angle, the lift–curve slope, and the drag coefficient at
zero angle were all higher as the advance ratio decreased.
The next configuration to be studied will be a mid-
wing which has the propeller located in the wing body
in a vertical direction. Perhaps, the performance of this
configuration might be better than for either the tractor
or pusher configuration because it benefits both the
upstream and downstream of the propeller.
Acknowledgments
The authors would like to thank the students of Aerospace
Engineering of Kasetsart University who helped us to per-
form the experimental set up.
Declaration of conflicting interests
The author(s) declared no potential conflict of interest
with respect to the research, authorship, and/or publi-
cation of this article.
Funding
The author(s) disclosed receipt of the following financial sup-
port for the research, authorship, and/or publication of this
article: The authors would like to thank the Graduate School
of Kasetsart University, Thailand. They appreciate their
funding and budget support for this research.
References
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Aerodynamic characteristics of a low aspect ratio wing
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Micro Air Vehicle 2013; 5: 245–260.
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Appendix
Notation
ac. aerodynamic center
A axial force (N)
AR aspect ratio
CD drag coefficient
CD0 zero-lift drag coefficient
CL lift coefficient
CLa lift–curve slope
CM pitching moment coefficient
CNp lateral propeller force coefficient
CT thrust coefficient
CX total longitudinal force coefficient
d propeller diameter (m)
D drag (N)
L lift (N)
J advance ratio
K factor of the drag polar curve
n propeller rotation speed (r/s)
N normal force (N)
Np lateral force (N)
M pitching moment (Nm)
Q torque (Nm)
r radial position (m)
Re Reynolds number
RPM propeller rotation speed (r/min)
S wing area (m2)
T thrust (N)
V freestream velocity (m/s)
VR slipstream resulting velocity (m/s)
w induced velocity in dynamic
propeller (m/s)
Chinwicharnam and Thipyopas 19
w0 static induced velocity (m/s)
x0.25c moment reference point with respect to the
0.25c (m)
X total longitudinal force (N)
aMAV model angle of attack (�)
astall stall angle (�)
� dynamic viscosity of the fluid (Ns/m2)
� air density (kg/m3)
20 International Journal of Micro Air Vehicles 8(1)