Cognition of Parameters' Role on Vertical Control Device for Aerodynamic Characteristics of Aircraft Using Data Mining

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Cognition of Parameters’ Role on Vertical Control
Device for Aerodynamic Characteristics of
Aircraft Using Data Mining
Kazuhisa Chiba1∗
, 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
Abstract
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.
∗kazchiba@uec.ac.jp
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1 Introduction
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[3]. 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[4]. 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[7].
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
2

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]
airfoil NACA0010
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[7].
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
3

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].
4

Figure 3: Schematic illustration of the system for the wind tunnel experi-
ment.
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
5

(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.
C□=□
1
2ρv2·S
,(1)
where, □denotes L,D, and Mp.
The Oswald efficiency factor eis selected as an indicator to preliminary
evaluate the aerodynamic performance of the aircraft[8]. The factor eis
calculated by using the following equation.
e=1
K·1
πAR ,(2)
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
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as function of CL.
CD=CD0+K·(CL−CL0)2.(3)
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
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Table 3: Comparison of efor several experimental conditions.
µ[mm] max e[-]
δ= 0 (fixed) δ(variable)
clean 0.6505
50 0.4531 0.4273
90 0.4535 0.4718
130 0.4875 0.5633
170 0.5471 0.6513
(a) (b)
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
each other.
4 Data-mining technique
In the present study, a self-organizing map (SOM)[5] is selected as a data-
mining technique because the primary objective of data mining is the ac-
8

quisition of global design information in order to implement the structuring
of design space. The previous study[1] 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
Viscovery R
⃝SOMine 4.0 plus produced by Eudaptics, GmbH[2]. 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.
9

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
10

CLCDCMp
(a) design requirements
µδα
(b) design parameters
σCLσCDσCMp
(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
design parameters.
The SOMs colored by CLand CDin Fig. 7(a) reveal that there is a
tradeoff between them. However, coloration patterns of CLand CDfor
11

CLCDCMp
(a) design requirements
µδ α
(b) design parameters
σCLσCDσCMp
(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
12

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
δ
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
13

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
requirements.
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
µδ
(a)
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CLCDCMp
(b) α=−6[deg]
CLCDCMp
(i) α= 8 [deg]
CLCDCMp
(c) α=−4[deg]
CLCDCMp
(j) α= 10 [deg]
CLCDCMp
(d) α=−2[deg]
CLCDCMp
(k) α= 12 [deg]
CLCDCMp
(e) α= 0 [deg]
CLCDCMp
(l) α= 14 [deg]
CLCDCMp
(f) α= 2 [deg]
CLCDCMp
(m) α= 16 [deg]
CLCDCMp
(g) α= 4 [deg]
CLCDCMp
(n) α= 18 [deg]
CLCDCMp
(h) α= 6 [deg]
CLCDCMp
(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.
15

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.
16

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
CD.
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
reduce CD.
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.
17

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.
6 Conclusions
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-
18

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
knowledge.
Acknowledgment
The present study was supported by Japan Society for the Promotion of Sci-
ence through a Grant-in-Aid for Challenging Exploratory Research 26630440.
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