Cognition of Parameters’ Role on Vertical Control
Device for Aerodynamic Characteristics of
Aircraft Using Data Mining
, Taiga Omori2, Yasuto Sunada2, and Taro Imamura2
1Graduate School of Informatics and Engineering,
The University of Electro-Communications,
1-5-1, Chofugaoka, Chofu, Tokyo 182-8585, Japan
2Department of Aeronautics and Astronautics,
The University of Tokyo,
7-3-1, Hongo, Bunkyo, Tokyo 113-8656, Japan
April 14, 2015
The new concept to place the vertical airfoil device as control sur-
face has been discovered so as to improve the aerodynamic performance
of aircraft. The concept was predicated on not only the several devices
as vortex generator and winglet but also the wing-mounted engine sys-
tem of the HondaJet. Thereupon, the wind tunnel experiment has
been implemented in order to investigate the inﬂuence of the verti-
cal control device with the symmetrical airfoil shape. Furthermore, a
self-organizing map as data mining has been performed for the experi-
mental data in order to qualitatively elucidate the correlations among
the aerodynamic performances as design requirements and the design
parameters to place the vertical control device. Consequently, it has
been revealed the design information regarding the intimate correla-
tions. Moreover, there is the sweet spot in the design space to improve
the aerodynamic performances.
Keyword: Vertical device; Control surface; Aerodynamics of aircraft;
Data mining; Self-organizing map.
Although the surface of the main wing of aircraft, especially upper wing
surface, is generally desirable to be smooth in ordinary design of an aircraft,
there are several exceptions to this universal tacit knowledge[6, 9], such as
small devices for ﬂow control. Honda Aircraft Company has designed and
developed a business jet aircraft named as the HondaJet. Despite the fact
that the devices are generally designed small on general knowledge even when
devices will be on the wing surface, the HondaJet mounts its engine over
the upper surface of the wing with the pylon. The design of the HondaJet
astonishingly reveals that the optimum location of the nacelle and the cross
section of the pylon exists to accomplish lower drag coeﬃcient compared
with the clean wing. This fact indicates that the devices on the wing
surface, whose size is independent on the convention of aircraft design, can
uncommonsensiblly improve the aerodynamic performance of aircraft.
Thereupon, in the present study, a new basic idea regarding a vertical
control device on the upper surface of the main wing will be proposed in
order to improve the aerodynamic performance of aircraft due to the ﬂow
control on the wing surface. The devices are expected to be also installed
on the trailing edge of the pylon in order to improve the aerodynamic per-
formance. Therefore, the objective of the present study is to elucidate the
eﬀectiveness on the aerodynamic performance regarding the control surface
which is vertically mounted on the wing. As a ﬁrst step, the wind tunnel ex-
periment is implemented in order to quantitatively reveal its eﬀectiveness.
As a second step, data mining is performed by using a self-organizing map
for the experimental data so that the global design information for the design
space will be also eﬃciently revealed. Especially, the keystone of the present
treatise corresponds to the second step. The objectives of the present data
mining are that signiﬁcant experimental conditions are eﬃciently addressed
from 103-order conditions. Furthermore, the obtained design knowledge will
be utilized in order to generate a wind tunnel model for the next-step experi-
ments so that a vertical control device is eﬃciently installed and its optimum
geometry will be designed.
2 Problem deﬁnition
The simple symmetrical aircraft model constructed by the main and tail
wings with rectangular planform and vertical control device is developed
in order to utilize in the wind tunnel experiment. The speciﬁcation of an
Table 1: Speciﬁcation of aircraft model for wind tunnel experiment.
component content data
length 370 [mm]
fuselage width 44 [mm]
height 55 [mm]
span length 404 [mm]
chord length 80 [mm]
main wing airfoil NACA2410
aspect ratio; AR 5.05 [-]
taper ratio 1.0 [-]
chord length 40 [mm]
vertical control device span height 40 [mm]
Table 2: Design parameters and their discretized design space.
description symbol design space
spanwise distance µ[mm] 10 ≤µ≤170 for every 10
deﬂection angle δ[deg] −10 ≤δ≤10 for every 2
angle of attack of body α[deg] −6≤α≤20 for every 2
aircraft model is shown in Table 1. The fuselage and tail wings constructed
by the plane surfaces are ﬁxed. The main wing itself is ﬁxed, however, the
vertical control device is shifted on the upper surface of the main wing.
Thereupon, the model geometry is deﬁned by the following three design
parameters. The ﬁrst is the spanwise distance from the root of the main wing
to the installed position of the vertical control device µ[mm]. The second is
the deﬂection angle of the vertical control device onto the upper surface of the
main wing δ[deg]. The illustrated description of these two design parameters
is shown in Fig. 1. The third is the angle of attack of the body α[deg]. The
design space of the each design parameter is summarized in Table 2. Since
the experiment cannot strictly set the values of the design parameters, the
three design parameters have not continuous but discretized values. µis the
distance between the root of the main wing (that is, body wall) and the
25% position of the mean aerodynamic chord for the vertical control device.
µmoves from 10 to 170 [mm] for every 10 [mm]. The two vertical control
devices are symmetrically set on the main wing. δis the deﬂection angle of
the vertical control device onto the main wing. The revolutionary center is
set on the 25% mean aerodynamic chord of the vertical control device. δis
Figure 1: Bird’s-eye illustration of overall geometry. The dotted lines on the
main wing describe the 17 installation positions (the length from the body
wall denotes µ) of the vertical control device colored by orange. The 25%
position of the mean aerodynamic chord for the vertical control device is
described by the white point in the orange color.
Figure 2: The wind tunnel model constructed by the separated wing blocks.
deﬁned to be the positive value when the trailing edge of the vertical control
device is installed on the outboard side shown in Fig. 1. δchanges from −10
to +10 [deg] for every 2 [deg]. Note that there are no experimental data in
the case of µof 10 [mm] and δof -10 [deg] because the vertical control device
interferes in the fuselage. αchanges from −6to +20 [deg] for every 2 [deg].
Figure 3: Schematic illustration of the system for the wind tunnel experi-
The total number of experimental conditions is 2,604. Geometry is designed
by using a computer-aided design software and it is outputted as the stereo
lithography data to generate the wind tunnel model.
The wind tunnel model is made from wood. It is constructed by several
elements in order to simply alter the geometry for all conditions of the wind
tunnel experiments. The appearance of the wind tunnel model and the
elements of the main wing are shown in Fig. 2. µcan be moved by inserting
blocks in the diﬀerent order along the spar. Each wing block is made by
using 3-dimensional printer. The vertical control device is also separately
constructed and it is attached onto the main wing with a screw so that δcan
be simply changed. There are gaps between the leading and trailing edges of
the vertical control device and the upper surface of the main wing, however,
they are negligible small.
3 Experimental result
The experiment was performed by using the blow-down wind tunnel at the
department of aeronautics and astronautics, the University of Tokyo. Its
(a) (b) (c) (d)
Figure 4: Polar curves. (a) clean conﬁguration, (b) installed conﬁguration at
µ= 50 [mm], (c) installed conﬁguration at µ= 130 [mm], and (d) installed
conﬁguration at µ= 170 [mm],
outward form has 600 [mm] height and width. The ﬂow velocity was set
to be 10 [m/sec] for all experimental conditions. The Reynolds number
based on the chord length as the reference one was approximately 5.0×
104. All of the experiments were carried out for 10 [sec] with the sampling
frequency of 1,000 [Hz]. Therefore, all of the data regarding the aerodynamic
performance obtained from the experiments are the time-averaged value of
10,000 points for 10 [sec]. Figure 3 shows the conceptual illustration of
the present measurement system for the present wind tunnel experiment. α
was controlled by the microcomputer using a proportional-integral-derivative
controller. Three aerodynamic performances of the body as a whole, the lift
L, the drag D, and the pitching moment Mp, are gauged by using the wind
tunnel balance. These performances are respectively transformed into the lift
coeﬃcient CL, the drag coeﬃcient CD, and the pitching moment coeﬃcient
CMp, which describe the following equation divided by the dynamic pressure
using the air density ρ, the velocity v, and the planform area of the main
wing Sas the reference one.
where, □denotes L,D, and Mp.
The Oswald eﬃciency factor eis selected as an indicator to preliminary
evaluate the aerodynamic performance of the aircraft. The factor eis
calculated by using the following equation.
where, the drag-due-to-lift factor Kis deﬁned as a leading coeﬃcient of the
quadratic approximation function due to CLunder the consideration of CD
as function of CL.
CD0denotes CDcaused by the other drag mechanisms. CL0is physically
caused by the vertical asymmetry such as a cambered wing and a ﬁnite angle
of incidence. When the lift of a wing is elliptically distributed along the span,
Kis deﬁned to be 1. AR denotes the aspect ratio of the main wing, whose
value is summarized in Table 1.
Figure 4 shows the polar curves under the several conditions. Figure
4(a) shows the repeatability of the polar curve for the clean conﬁguration
implemented three times on diﬀerent days. Since the three lines precisely
correspond each other, the reproducibility of the present experiment can be
elucidated. When the Kis calculated by using eq. (3) for the average of
three data shown in Fig. 4(a), the wind tunnel model without the vertical
control device found to be e= 0.6505. Note that the correlation between
the dotted line and the other three lines in Fig. 4 shows the accuracy of K.
Figure 4(a) shows that the curve generated by the quadratic approximation
function exactly describes the polar curves by the experiment.
Figures 4(b), (c), and (d) respectively show the polar curves by changing
δfrom −10 to +10 [deg] under the conditions of µof 50 [mm], 130 [mm],
and 170 [mm]. The dotted curve is quadratic approximation as eq. (2) with
the points of −4≤α≤12 [deg]. Figure 4 reveals that the shape of polar
curve becomes similar to that for the clean conﬁguration as µis larger.
The curvature of polar curve becomes larger as µis smaller. Although CD
is moved to right direction due to CDby the vertical control device, the
geometry of the polar curve is similar in the case of µof 170 [mm]. Although
CDat δ= 0 is found to be low around low angle of attack, there are δthat
gives larger CL/CDthan that of δ= 0, when αis higher than 6 [deg]. When
optimum δis selected according to the angle of attack, the data is on the
envelope curve and ewill be improved. The results based on this procedure
are summarized in Table 3. In both cases of µ= 130 and 170 [mm], eis
improved. Especially, it is almost the identical as the clean conﬁguration for
the case of µ= 170 [mm].
On the other hand, in the cases of µ= 50 and 90 [mm], there is not
as much improvement as cases of µ= 130 and 170 [mm]. In Fig. 4(d), the
case of δ= 0 gives the best CL/CDexcept the cases of high angle of attack.
In Fig. 5, there is considerably the interference between δand CMp , and
also between δand CL. When δis positive value, CLtends to be lower
and CMp tends to be higher. In contrast, the negative δoppositely aﬀects
on CLand CMp. The reason of these eﬀects is that the vortex generated
Table 3: Comparison of efor several experimental conditions.
µ[mm] max e[-]
δ= 0 (ﬁxed) δ(variable)
50 0.4531 0.4273
90 0.4535 0.4718
130 0.4875 0.5633
170 0.5471 0.6513
Figure 5: Comparison of the aerodynamic performance of the installed con-
ﬁguration at µ= 50 [mm]. (a) CL-αand (b) CM p-α.
from the tip of the vertical control device passes in the vicinity of the tail
wings, when µis small value such as µ= 50 [mm]. Changing the value of δ
from positive to negative reverses the rotational direction of the tip vortex
by the vertical control device so that the interference for CLand CMp is also
opposite. There was little improvement on eunder the condition of µ= 50
[mm] conﬁguration because the positive eﬀect of δ≥0and negative eﬀect
of the tip vortex on the vertical control device shown in Fig. 5(a) cancelled
4 Data-mining technique
In the present study, a self-organizing map (SOM) is selected as a data-
mining technique because the primary objective of data mining is the ac-
quisition of global design information in order to implement the structuring
of design space. The previous study indicated that SOM extracted the
global design information for whole design space. The distinguishing feature
of SOM is the generation of a qualitative description. The advantage of this
method contains the intuitive visualization of two-dimensional colored maps
of design space using bird’s-eye-views. As a result, SOM reveals the tradeoﬀs
among objective functions. Moreover, SOM addresses the eﬀective design
parameters and also reveals how a speciﬁc design parameter gives eﬀects on
objective functions and other design characteristics. One SOM is colored for
one variable of objective function, design parameter, and other characteristic
value so that the coloration pattern is compared with each other. Therefore,
data mining using SOM might have a disadvantage to overlook important
correlation in the problem with a large number of objective functions and
design parameters. Since the present study has a total number of 9 at most
among the design requirements, design parameters, and other variables that
the inﬂuence will be observed, SOM is suﬃcient for the data mining manner.
In the present study, SOMs are generated by using commercial software
⃝SOMine 4.0 plus produced by Eudaptics, GmbH. The unique-
ness of the map generated by SOMine is assured due to Kohonen’s Batch
SOM algorithm and search of the best-matching unit for all input data and
Figure 6: Comparison example of colored SOMs for minimization problem
with three objective functions as f1,f2, and f3. Red describes high value
and blue is low one.
the adjustment of weight vector near the best-matching unit. The decoding
manner of SOM is brieﬂy explained by using Fig. 6. This ﬁgure is assumed to
be SOMs colored by three objective functions on the minimization problem
of three objective functions. The generated SOM is made from hexagonal
grid, which has the values of objective functions and design parameters as
a vector quantity. Grids are distributed on a two-dimensional rectangular
surface by the aﬃnity of each objective-function value. Thereupon, grids
with high aﬃnity of each objective-function value clusters around a grid.
There is no physical import on the vertical and horizontal lines of SOM.
The comparison among SOMs to be colored by each vector quantity in each
grid intuitively reveals the correlations among each vector quantity. There
is similar coloration pattern between SOMs for f1and f2shown in Fig. 6.
This comparison shows that one objective function absolutely has a low
value, when another objective function has low value. Moreover, one ob-
jective function absolutely has high value, when another objective function
has high value. That is, this comparison indicates that there is no tradeoﬀ
between f1and f2. On the other hand, f3absolutely becomes large, when
f1becomes small, and vice versa. This comparison proves to be a severe
tradeoﬀ between f1and f3.
5 Data-mining result
The coloration pattern of SOM depends on indicator. Multiobjective op-
timization problems generally use objective functions as the indicator to
generate SOM. However, both of the design requirements, i.e., CL,CD, and
CMp and the design parameters have a major role in the present problem.
Thereupon, as the ﬁrst step, the SOM which the design requirements take
charge of the indicator will be observed. As the second step, the SOM which
the design parameters take charge of the indicator will be observed in this
chapter. The especial design parameters to improve the aerodynamic per-
formances will be speciﬁed so as to address the experimental condition and
to eﬃciently reveal the ﬂow mechanism.
5.1 Case to generate using design requirements
Figure 7 shows the SOM generated by the values of the three design require-
ments. As this SOM learning is implicated based on the values of the design
requirements as the indicator for the similarity on the neural network, the
SOMs colored by the design requirements have absolutely gradation shown
in Fig. 7(a). The SOM colored by design requirement can generally indicate
(a) design requirements
(b) design parameters
(c) standard deviation σas other indicator
Figure 7: SOM generated by design-requirements values.
not only tradeoﬀ information but also optimum and pessimum direction on
SOM due to the gradation. In addition, the directions of the inﬂuence of
design parameters for design requirements can be observed by comparison
between the SOMs colored by the design requirements and those by the
The SOMs colored by CLand CDin Fig. 7(a) reveal that there is a
tradeoﬀ between them. However, coloration patterns of CLand CDfor
(a) design requirements
(b) design parameters
(c) standard deviation σas other indicator
Figure 8: SOM generated by design-parameters values.
both the maximum and minimum directions are diﬀerent. The compromise
design region can be relatively found out on the SOM. The SOM colored by
CMp in Fig. 7(a) reveals that the SOM’s region to be the low value of CMp
corresponds to that to be the high value of CD. On the other hand, although
the SOM’s region to be the high value of CMp exists the bottom right on
the SOM, the coloration pattern of it is unique. Note that CM p should be
generally zero for the trim of the aircraft. The trim is practically gained by
controlling the elevators. Since the elevators of the present body are ﬁxed,
the present CMp cannot indicate the optimum and pessimum directions.
Correlations between CMp and the other two aerodynamic characteristics as
CLand CDare merely observed.
The SOMs colored by the three design parameters as µ[mm], δ[deg],
and α[deg] are shown in Fig. 7(b). The SOM colored by µreveals that µ
does not have direct inﬂuence on the three design requirements. Although
there is a possibility that the combination between µand δgives the eﬀects
on the design requirements, Figs. 7(a) and (b) does not indicate it. The
SOM colored by δreveals that the low value of δgives an eﬀect on the low
value of CD. The high value of δdoes not directly give eﬀects on the three
design requirements. The SOM colored by αreveals that the high value of α
directly aﬀects on the high value of CDand also the low value of αdirectly
gives an eﬀect on the low value of CL. Since αgenerally has the eﬀects on
the aerodynamic performance, these results make sense. Since the coloration
pattern shown in Figs. 7(a) and (b) depends on α,αshould be omitted so
that the inﬂuences of µand δare observed.
Figure 7(c) shows the SOMs colored by the standard deviation σfor the
three design requirements as CL,CD, and CMp . The present σis deﬁned
as the standard deviation for the data of 10,000 points for 10 [sec] in an ex-
perimental condition. These ﬁgures reveal that these have similar coloration
pattern, and σhas high value when αbecomes high. This fact suggests that
σincreases after the stall. The SOM generated by the three design param-
eters as µ,δ, and αis prepared in Fig. 8 in order to directly observe the
inﬂuence of them on the three design requirements. The coloration patterns
of CLand CDreveal that there is no regularity for those of µand δ. That is,
the coloration patterns of the design requirements indicate that the design
requirements strictly depend on α. Thereupon, the inﬂuence of αon the
three design requirements should be erased in order to directly observe the
inﬂuence of µand δ.
5.2 Case to generate using two design parameters as µand
The SOM generated by µand δis shown in Fig. 9. Figure 9(a) shows
the SOMs colored by µand δthemselves, which are the straightforward
coloration patterns. The coloration pattern for µis from upper to bottom
and the upper region has high value of µand the bottom region has low
value of µ. On the other hand, the coloration pattern for δis from left to
right. The left region has high value of δand the right region has low value
of δ. Figures 9(b) to (o) show the SOMs colored by CL,CD, and CMp for
each αfrom −6[deg] to 20 [deg] with 2 [deg] interval. The inﬂuence of the
combination between µand δon each design requirement will be observed
step by step. Note that the results of the latest calibration experiment of
the wind tunnel balance show to ensure the suﬃcient accuracy of CDfor the
narrow range of CDin Fig. 9. Therefore, discussion which Fig. 9 is employed
can be implemented because Fig. 9 has the signiﬁcant diﬀerence of the design
5.2.1 Eﬀectiveness on CL
In the ﬁrst place, inﬂuence on CLwill be observed. The eﬀectiveness of the
design parameters on CLis roughly clustered for three αregions as α≤0,
2≤α≤12, and α≥14 [deg].
In the case of α≤0[deg], speciﬁc combinations of µand δgive eﬀects
on CL. The combinations of µ≥140 [mm] and δ≥8[deg], and the µ≤90
[mm] and δ≤0[deg] give the eﬀect on increasing CL. Eﬀectiveness on CLis
stronger as αis greater in the case of the former combination. On the other
hand, the combinations of µ≥150 [mm] and δ≤ −8[deg], and µ≤40 [mm]
and δ≥6[deg] give the adverse eﬀect on decreasing CL. The magnitude of
the latter adverse eﬀectiveness is stronger than that of the former one. The
adverse eﬀectiveness on CLis weaker as αincreases in the former case. That
is, the eﬀectiveness on the increase of CLin the case of high µis stronger as
αincreases. Since the separation near the tip of the main wing is restrained
when the vertical control device is in the vicinity of there, CLincreases. In
addition, the main wing generates the positive CLat greater than αCL0. The
clean conﬁguration does not have this eﬀectiveness. On the other hand, the
latter adverse eﬀectiveness is independent on α. When the vertical control
device with +δinstalls in the vicinity of the fuselage, the fuselage and the
(i) α= 8 [deg]
(j) α= 10 [deg]
(k) α= 12 [deg]
(e) α= 0 [deg]
(l) α= 14 [deg]
(f) α= 2 [deg]
(m) α= 16 [deg]
(g) α= 4 [deg]
(n) α= 18 [deg]
(h) α= 6 [deg]
(o) α= 20 [deg]
Figure 9: SOMs, (a) colored by each value of the two design parameters as
µand δ, (b) to (o) colored by the design requirements at each α.
device generate quasi-throat ﬂow. Since it is diﬃcult to ﬂow on the main-
wing region where the fuselage and the device sandwich, this region is not
functioning as a wing. Therefore, CLis reduced as much.
In the case of 2≤α≤12 [deg], the combinations between µ≥160 [mm]
and δ≥0[deg] at 2≤α≤6[deg], and between µ≥160 [mm] and all δ
at α≥8[deg] give the eﬀect on increasing CL. When the vertical control
device installs near the wing tip, the device functions as winglet. Therefore,
CLincreases under the condition. The eﬀectiveness under the condition that
the vertical control device is near the tip disappears in the case of over α
of 14 [deg] because of the stall. The combination between µ≤100 [mm]
and δ≥6[deg] aﬀects on decreasing CL. This eﬀectiveness is weaker as α
increases. The combination between µ≤90 [mm] and δ≤ −2[deg] also
aﬀects on decreasing CL. This eﬀectiveness is stronger as αincreases. When
the vertical control device installs around the middle of the wing, the device
discourages the wing function. Since the wetted area of the vertical control
device for the uniform ﬂow is especially larger as |δ|becomes larger, the
adverse eﬀectiveness on CLis strong.
In the case of α≥14 [deg], µ≥140 [mm] aﬀects on decreasing CL.
Especially, δ≥0[deg] at αof 14 [deg], δ≥0[deg] and δ≤ −6[deg] at
αof 16 [deg], and δof roughly 0 [deg] at αof 18 and 20 [deg] have this
eﬀectiveness. Since the vertical control device with +δin the vicinity of the
wing tip ampliﬁes the tip stall, CLsharply decreases. On the other hand,
the combination between µ≤40 [mm] and δ≥4[deg] gives the eﬀect on
increasing CL. The upper limit of µto increase CLgrows as αincreases.
In addition, the combinations between µ≤70 [mm] and δ≥0[deg] at α
of 16 [deg], between 30 ≤µ≤110 [mm] and δ≥ −2[deg] at αof 18 [deg],
and between 50 ≤µ≤130 [mm] and δ≥ −4[deg] also give the eﬀect on
increasing CL. Since the vertical control device at the middle of the wing
exists the inside of separation due to the stall, the device reduces the pressure
of its wake. As a result, CLincreases. The combination between µ≤50
[mm] and δ≤ −2[deg] at α≥16 [deg] gives the eﬀect on increasing CL.
Since the vertical control device with −δmaintains the wing tip vortex, CL
increases. CLis easily increased by µand δin the case of high α.
5.2.2 Eﬀectiveness on CD
In the second place, inﬂuence on CDwill be observed. The eﬀectiveness
of the design parameters on CDis clustered for three αregion as α≤12
[deg], αof 14 [deg], and α≥16 [deg]. However, since µprimarily has the
eﬀectiveness on CD, the results will be summarized by using µ.
µof 150 [mm] always gives the eﬀect on decreasing CD. The eﬀectiveness
is not dependent on α. The combination between µof 150 [mm] and −6≤
δ≤4[deg] especially gives more powerful eﬀect on decreasing CD. The
magnitude of this eﬀectiveness is similar among the cases at α≤4[deg]
and α≥16 [deg]. The magnitude of this eﬀectiveness of 0< δ ≤4[deg] is
stronger at α≤2[deg]. In contrast, that of −6≤δ≤0[deg] is stronger
at 4≤α≤12 [deg]. The magnitude of this eﬀectiveness at αof 14 [deg]
is the weakest due to the existence of another combination between µand
δto reduce CDmore. The separation in the vicinity of the tip of the main
wing will be restrained in the case at 150 [mm]. The ﬂow visualization of the
three-dimensional space should be additionally performed in order to reveal
the physical mechanism that µof 150 [mm] has the eﬀectiveness on reducing
µ≤20 and 70 [mm] also give the eﬀect on decreasing CD. The eﬀec-
tiveness does not depend on α. The separation which occurs due to the
interference with the fuselage will be restrained in the case at µ≤20 [mm]
position. On the other hand, the wake of the vertical control device interferes
in the tip of the horizontal tail wing in the case at µof 70 [mm] position.
Both of these cases should not have a large |δ|because of the larger wetted
area of the vertical control device for the uniform ﬂow.
In contrast, µof 40 [mm] aﬀects on increasing CD. The inﬂuence does
not depend on α. Since the wake of the vertical control device interferes the
horizontal tail wing, the CDof it increases. The ﬂow visualization of the wake
of the device should be implemented. In addition, CDof each component
should be elucidated by using computational ﬂuid dynamics analysis.
δ≥8[deg] and δ≤ −8[deg] aﬀects on increasing CDalthough µof 70
and 150 [mm] restricts the inﬂuence because the wetted area of the vertical
control device for the uniform ﬂow becomes large. Thereupon, a large num-
ber of |δ|such as δ≥8[deg] and δ≤ −8[deg] should not be set in order to
The case of αof 14 [deg] has unique eﬀectiveness on CD. The combination
between µaround 60 [mm] and δof −4[deg] gives the eﬀect on decreasing
CD. Since the wake of the vertical control device interferes the tip of the
horizontal tail wing, the ﬂow around the horizontal tail wing will be changed.
On the other hand, the combination between µof 10 [mm] and δ≥8[deg]
and δ≤ −6[deg] aﬀects on increasing CDin the case of α≥16 [deg]. The
wing tip vortex is broke down because the vertical control device interferes it.
The circumstantial physical mechanism to give the inﬂuence on CDshould
be elucidated by using the ﬂow visualization.
5.2.3 Eﬀectiveness on CM p
In the third place, inﬂuence on CM p will be observed. The eﬀectiveness of
the design parameters on CMp is clustered for three αregions as α≤2,
4≤α≤12, and α≥14 [deg], whose clustering is similar to that for CL.
The inﬂuence on CMp is easily understood because it depends on α.
In the case of α≤2[deg], the combination between µaround 50 [mm] and
δ≥4[deg] aﬀects on increasing CMp. On the other hand, the combination
between µaround 60 [mm] and δ≤ −8[deg] aﬀects on decreasing CMp .
This change of CMp is explained by the function on the main-wing region
where the fuselage and the vertical control device sandwich, that is similar
mechanism of CL.
In the case of 4≤α≤12 [deg], the eﬀectiveness is clustered by using
µ. The case of µ≥150 [mm] aﬀects on increasing CM p. It is independent
of δ. Since this area on SOM has large CLand small CD,CM p naturally
increases. The combination between µaround 50 [mm] and δ≥4[deg]
aﬀects on decreasing CMp. The result is occurred by the similar mechanism
in the above case of α≤2[deg]. The combination between µ≤90 [mm] and
δ≤ −4[deg] also aﬀects on decreasing CMp. Since the wake of the vertical
control device interferes the tip of the horizontal tail wing, the tip vortex of
the horizontal tail wing is induced. Therefore, the total CM p is reduced.
In the case of α≥14 [deg], the combination between 50 ≤µ≤80
[mm] and δ≤ −4[deg] aﬀects on increasing CMp. This is caused by the
interference of the wake of the device with the tip of the horizontal tail
wing. On the other hand, the combination between 40 ≤µ≤70 [mm] and
δ≥4[deg] aﬀects on decreasing CMp. The result is occurred by the similar
mechanism in the above case of α≤2[deg]. Moreover, µ≥140 [mm] also
aﬀects on decreasing CMp except for the case of αof 20 [deg]. This does not
depend on δ. The result is induced by decreasing CL.
CMp directly depends on CL,CD, and α. In addition, the trim of the
aircraft is practically gained to control elevators. Thereupon, it is consid-
erable that the design knowledge regarding CLand CDis primary and the
design knowledge regarding CMp is secondary.
The new concept to place the vertical airfoil device as control surface has
arrived in so as to improve the aerodynamic performance. The wind tunnel
experiment has been implemented in order to investigate the inﬂuence of the
vertical control device with symmetrical airfoil shape. Moreover, data min-
ing has been performed by using a self-organizing map for the experimental
data in order to qualitatively reveal the correlations among the aerodynamic
performances and the design parameters to place the vertical control device.
Consequently, it has been revealed the correlations among them. Further-
more, there is a sweet spot, where is at µaround 150 [mm] and −4≤δ≤4
[deg], in the present design space. In addition, the especial design parame-
ters to improve the aerodynamic performance have been speciﬁed by using
the data mining so that the detailed ﬂow condition is observed. The three-
dimensional geometry of vertical control device in the sweet spot will be
optimized as the subsequent design phase based on the extracted design
The present study was supported by Japan Society for the Promotion of Sci-
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