handytjenathofinal

1
LEMBAR PENGESAHAN INDUSTRI
Telah disetujui dan disahkan oleh
PT. DIRGANTARA INDONESIA(IAe)
Bandung, 28 Juli 2016
Aileron Hinge Moment and Optimization due to Varying Control Surface
Sizing
Menyetujui:
PEMBIMBING
MOCHAMAD DADY MA’MUN
NIK. 930427
ATASAN PEMBIMBING
D.JUNITO TIKUPASANG
NIK. 1930895
Mengetahui:
An. KEPALA DIVISI PENGEMBANGAN SDM
MANAGER PENDIDIKAN DAN PELATIHAN
Dipl. Ing. Imam Suwarto, MSAe.
NIK. 822811

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Aileron Hinge Moment and Optimization due to
Varying Control Surface Sizing
Handy Tjenatho
PT. Dirgantara Indonesia
Arizona State University, Tempe, Arizona 85281
The main objective of this study was to determine the required pilot’s stick force for N219-
B07 aircraft while varying the size of aileron, nose balance, tabs and horn balance. It was
important to obtain lower stick force so that surface deflection could be controlled easily.
Surface deflection of the wing was necessary for aircraft to pitch and roll. In order to obtain
the required stick force, the hinge moment coefficient had to be found. The steps used to
determine the stick force of B219-B07 aircraft were introduced by the book written by Dr. Jan
Roskam. In order to further prove the calculation, the stick force at 5 different possible
cruising aircraft conditions were determined. The stick force at these conditions had to be
lower than the required regulation from CASR23 (below 50lbs). Since the stick force was
dependent on the horn and nose balance ratio, the plots of force vs nose balance ratio and
force vs horn balance ratio would then be drawn. These plots were useful in determining the
required ratio of the nose and horn balance in order to prevent the stick force to be more than
50lbs. The results obtained from this study showed that the size of the flaperon and tabs had
to be 60% and 20% of the total chord respectively with nose balance ratio of 0.27.

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Table of Content
I. Nomenclature 4
II. Introduction 5
III. Procedure 7
IV. Result 13
V. Conclusion and Recommendation 19
VI. Reference 21
VII. Appendix 22

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Nomenclature
MAC = mean aerodynamic chord
𝐶ℎ = coefficient of hinge moment
𝐶ℎ𝑜 = initial coefficient of hinge moment
𝐶ℎ𝛼 = coefficient of hinge moment due to angle of attack
𝐶ℎ𝛿 = coefficient of hinge moment due to control surface deflection
𝐶ℎ𝛿𝑡 = coefficient of hinge moment due to ta deflection
𝛼 = angle of attack
𝛿 = control surface deflection
𝛿𝑡 = tab deflection
𝐴𝑅 = aspect ratio
(𝐶ℎ𝛼)𝑀 = coefficient of hinge moment due to Mach number
M = Mach number
𝑐ℎ𝛿𝑎 = coefficient of hinge moment due to aileron deflection
𝛼𝛿 = angle of attack due to surface deflection
𝐶𝑏 = distance from hinge line to the leading edge of control surface
𝐶𝑓 = distance from hinge line to the trailing edge of control surface
𝐶ℎ𝛿𝑠𝑡 = coefficient of hinge moment due to servo deflection
𝛿𝑠𝑡 = servo tab deflection
𝛼𝛿𝑠𝑡 = tab deflection
𝑐𝑙𝛼 = lift-curve slope
HM = hinge moment
𝐶𝑎 = aileron chord
𝑆𝑎 = aileron surface area
ƿ = density
𝐹 = force
𝐺𝑅 = gear ratio
𝑉𝑀𝐶𝐴 = minimum control speed in free air
𝑉 = velocity
𝐾𝐸𝐴𝑆 = equivalent airspeed in knot

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I. Introduction
Hinge moment is one of the vital components which has to be considered while designing an
aircraft. Each control surface in an aircraft would have hinge moments. These control surfaces
may include aileron, trim tab, rudder, elevator, etc. The hinge moments produced by the hinges
due to particular deflection of control surface decide the force needed by the pilot to control the
aircraft in lateral or longitudinal direction. This happens due to the fact that the pilot has to counter
the moment produced by the hinges in order to deflect the surfaces so that the pilot could maintain
the control over the aircraft easily. As the hinge moment increases, it requires the pilot to produce
more force on the stick in order to obtain pitching, rolling or yawing maneuver.
During the time spent at PT. Dirgantara Indonesia, a task of determining the hinge moment of
N219-B07 due to varying size of aileron, nose balance, tabs and horn balance had to be solved.
Deflections of surfaces in wing such as ailerons and tabs were responsible in allowing the aircraft
to pitch and roll. The hinge moment analysis was done three-dimensionally by taking into account
the actual geometry of the control surface prepared in a report done by Farida Rachmayanti with
a title “N219 B12 Geometrical Definition” (1). The wing plan-form could be seen on table 1.

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Table 1 and 2 showed the basic wing
geometry which were necessary to predict the
hinge moment of the aileron. The information
given would then be used to approximate the force
required for the pilot to deflect control surfaces in
order to create maneuvers. If necessary, the wing
and aileron planforms could be altered in order to
give a better maneuver to the aircraft.
In order to assist the stability and control over
N219 aircraft, servo and trim tabs were installed on both wings. Servo tab was the surface which
helped the aircraft in reducing the stick force by deflecting the surface itself opposite to the
direction of aileron deflection. Servo tab was important especially for small aircraft to improve the
pitching ability. This was because smaller aircraft could not fully rely on its elevator to produce
pitching moment due to shorter moment arm. On the other hand, trim tab was the surface that
helped the aircraft in reducing its stick force back to zero. Trim tab was used when the aircraft
was flying steadily. The graphical representation of the servo and trim tabs could be seen from
fig. 1.
Table 1. N219 B12 Wing Planform(1)
Table 2. N219 Flaperon Geometry(1)

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II. Procedures
In order to predict the force required by the pilot to deflect a control surface, the hinge moment
coefficient caused by deflecting the particular surface has to be determined. The total hinge
moment at a particular control surface could be modeled as:
𝐶ℎ = 𝐶ℎ𝑜 + 𝐶ℎ𝛼 . 𝛼 + 𝐶ℎ𝛿. 𝛿 + 𝐶ℎ𝛿𝑡. 𝛿𝑡(2)
(1)
The equation shown in eq.1 could be used to predict the hinge moment at any control surface
including rudder, elevator and aileron. For wings specifically, five different hinge moment
components have to be taken into consideration, such as initial hinge moment, hinge moment
due to change in angle of attack, hinge moment due to deflection of aileron, trim tab and servo
tab. By looking at eq. 1, it could be said that in order to reduce the total hinge moment of the
control surface, the values of 𝐶ℎ𝛼, 𝐶ℎ𝛿 or 𝐶ℎ𝛿𝑡 had to be reduced. This could be done by
modifying the surface geometry such as the area of flaps and tabs, and the aspect ratio and
sweep of the wing. This statement could be further supported by looking at these following
equations:
𝐶ℎ𝛼 = [
𝐴𝑅 𝑐𝑜𝑠˄
𝑐
4
𝐴𝑅 + 2𝑐𝑜𝑠˄
𝑐
4
] (𝐶ℎ𝛼)𝑀 + 𝛥𝐶ℎ𝛼(2) (2)
Figure 1. N219 2D Flaperon Geometry(1)

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Where,
(𝐶ℎ𝛼)𝑀 =
( 𝐶ℎ𝛼)𝑏𝑎𝑙
(1−𝑀2)0.5(2)
(3)
In which, the value of ( 𝐶ℎ𝛼)𝑏𝑎𝑙 with varying balance ratio had been tested out by Dr. Jan Roskam.
Dr. Jan Roskam tested different shapes of surface nose. This was done due to the fact that
different nose shapes could affect the fluid flow along the aileron in different ways. The value of
( 𝐶ℎ𝛼)𝑏𝑎𝑙 was modeled as could be seen from fig. 2 (Roskam).
Same thing was done when 𝐶ℎ𝛿𝑎 was being calculated, where:
𝐶ℎ𝛼 = (𝑐𝑜𝑠˄
𝑐
4
) (𝑐𝑜𝑠˄ℎ𝑙)
∗ [(𝑐ℎ𝛿𝑎)𝑀
+ 𝛼𝛿(𝐶ℎ𝛼)𝑀 {
2 cos
𝑐
4
𝐴𝑅 + 2𝑐𝑜𝑠˄
𝑐
4
}]
+ 𝛥𝑐ℎ𝛿𝑎(2)
(4)
In which, the value of (𝐶ℎ𝛼)𝑀 was modeled from eq. 3, (𝑐ℎ𝛿𝑎)𝑀 was modeled from eq. 5 and
𝛼𝛿 was extracted from fig. 4.
(𝐶ℎ𝛿)𝑀 =
( 𝐶ℎ𝛿)𝑏𝑎𝑙
(1−𝑀2)0.5(2)
(5)
Where the value of ( 𝐶ℎ𝛿)𝑏𝑎𝑙 was extracted from, fig. 3

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From fig. 2 and fig. 3, it was clearly shown
that the nose balance of the control surface
played an important role in determining 𝐶ℎ𝛼 and
𝐶ℎ𝛿. Although it seemed that higher nose
balance would result in better 𝐶ℎ𝛼 and 𝐶ℎ𝛿, an
important attention should be taken to the shape
of the surface nose. Higher nose balance would
mean that the length of Cb would be longer than
the length of Cf which might cause a disturbance
in the flow of the fluid(3). A graphical
representation of high nose balance could be
seen in fig. 5.
By calculating the hinge moment due to the effects of angle of attack and aileron deflection,
the prediction of hinge moment trend with varying angle of attack could be determined. However,
this design of the wing would not be as efficient due to the fact that servo tab was not included in
the calculation. According to CASR certification, N219 shall have a maximum stick force of 50lb
for the pilot to produce(3). Servo tab’s main task was to reduce the force produced by the pilot by
Figure 2. Plots of ( 𝑪𝒉𝜶)𝒃𝒂𝒍 vs Balance Ratio(2) Figure 3. Plots of ( 𝑪𝒉𝜹)𝒃𝒂𝒍 vs Balance Ratio(2)
Figure 4. Plots 𝜶𝜹 vs Flap Deflection(2)

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deflecting its surface opposite to the direction of
aileron deflection. For N219 specifically, the gear
ratio of aileron deflection to servo tab deflection
was 0.5. This was proven to be efficiently
reducing the hinge moment, which would also
then reduce the force required for the pilot to give
a pitching moment to the aircraft. The graphical
representation of servo tab could be seen from
fig. 6. The hinge moment coefficient caused by
servo tab could also be modeled as:
𝐶ℎ𝛿𝑠𝑡 = (𝐶ℎ𝛿𝑠𝑡)𝑐𝑙, 𝛿𝑎 − {(𝐶ℎ𝑐𝑙)𝛿𝑠𝑡, 𝛿𝑎}
∗ {(𝑐𝑙𝛼)𝛿𝑠𝑡, 𝛿𝑎}
∗ {(𝛼𝛿𝑠𝑡)𝑐𝑙, 𝛿𝑎} (2)
(6)
Where (𝐶ℎ𝛿𝑠𝑡)𝑐𝑙, 𝛿𝑎, (𝐶ℎ𝑐𝑙)𝛿𝑠𝑡, 𝛿𝑎 and (𝛼𝛿𝑠𝑡)𝑐𝑙, 𝛿𝑎 could be extracted from fig. 7, fig. 8 and fig. 9
respectively. From the airfoil selection, it was also known that the value of (𝑐𝑙𝛼)𝛿𝑠𝑡, 𝛿𝑎 was set to
be 0.12(3).
Figure 5. Graphical Representation of High
Nose Balance
Figure 7. Plots of (𝑪𝒉𝜹𝒔𝒕)𝒄𝒍, 𝜹𝒂 vs Cf/C(2)Figure 6. Servo tab deflection(3)

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The figures shown from fig. 7 to fig. 9 clearly showed that the values of (𝐶ℎ𝛿𝑠𝑡)𝑐𝑙, 𝛿𝑎,
(𝐶ℎ𝑐𝑙)𝛿𝑠𝑡, 𝛿𝑎 and (𝛼𝛿𝑠𝑡)𝑐𝑙, 𝛿𝑎 were related to the size of the servo tab’s and flap’s sizes.
When the aircraft was supposed to fly steadily, the pilot would need to have a trim
condition in order to lessen their work. This could be done by the addition of trim tab. By trimming
the aircraft, the pilot would produce zero force on the stick which made the aircraft to be in a stick-
free condition. The same calculation model as servo tab was used while calculating the hinge
moment coefficient of the trim tab. The dimension of the trim tab relative to the chord length was
similar to the servo tab. The only difference was that trim tab deflection might not necessarily be
in a ratio of aileron deflection. Trim tab could be set in any angle of deflection as long as it would
bring the force required by the pilot back to zero. It was also important to know that trim tab shall
not be deflected for more than 15 degrees. When an aircraft had to have trim tab deflected for
more than 15 degrees, the aircraft was said to be not efficient in terms of its stability.
By having these done, plots could be generated by using eq. 1 where cho was set to be 0.0013.
This was necessary in order to find the trend of hinge moment coefficient along different angles
of attack. The effect of different aileron deflections might also be plotted under one plot to see the
difference between each deflection.
Hinge moment of the aileron could further be determined once its coefficient had been found
out. It could be done by:
Figure 8. Plots of (𝑪𝒉𝒄𝒍)𝜹𝒔𝒕, 𝜹𝒂 vs Cf/C(2) Figure 9. Plots of (𝜶𝜹𝒔𝒕)𝒄𝒍, 𝜹𝒂 vs Ct/C(2)

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𝐻𝑚 = 𝑐ℎ ∗ ƿ ∗ 𝐶𝑎 ∗ 𝑆𝑎(3)
(7)
Once the hinge moment had been found, the pilot stick force could be calculated by:
𝐹 = 𝐻𝑚 ∗ 𝐺𝑅(3)
(8)
With this being done, plots of force vs cb/cf with different tab sizes could be drawn to determine
the tab and aileron’s nose sizes that would perfectly match the trim condition as well as the
regulation that requires a maximum pilot stick force of 50lbs (CASR 23). It was advised that the
nose balance ratio shall be as low as possible to prevent flow disturbance. The size of the aileron
could also be modified in order to further support the required objectives. In order to further
convince the result, different horn balance sizes could be studied. This was done by plotting force
vs cf in order to point out the best size of flap with regards to the size of the local chord.
The credibility of the results obtained could be tested by calculating the force at certain
conditions which the aircraft was usually flying in. These conditions might include when the aircraft
was flying at VMCA, crosswind, roll and DA trim.
The aircraft flying at this condition had different flying characteristics. The important variables
that varied were aileron deflection, speed and the angle of attack. These variables were one of
the vital components which decided the amount of stick force required for the pilot to create
maneuver. It was important to ensure that the aircraft which was flying at these conditions had
similar or better characteristics as what was being determined in the general observation done by
using eq. 1 to eq. 8. For better time management, calculation of hinge moment for roll rate
requirement could be the only condition which was being observed. This was possible to be done
due to the fact that the hinge moment produced at this condition was the highest among the other
conditions. This also meant that during this condition, the possibility for the force to be greater
than what was expected at the same nose balance ratio could be larger. In order to calculate the
force from eq. 8, the calculation of hinge moment had to be done by using eq. 7 where the value
of ch was being extracted from the plot of cha vs alpha with varying aileron deflections. The main
aim of calculating the hinge moment and force at these conditions was just to make sure that the

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aircraft would still fulfill the trim and regulation requirements while the aircraft was flying at any
specific case.
III. Results
Using the methods done by Dr. Jan Roskam, the following results were obtained,
Shown in fig. 10 and fig. 11 were the trend of
aileron hinge moment coefficient with increasing
angle of attack and varying aileron deflection. As
could be seen, the magnitude of the coefficient
lowered by small amount when tabs were
installed. The plots also showed that the
magnitude of its hinge moment would tend to increase as the angle of attack moved away from 0
degree. When the aileron was deflected in a positive angle, the hinge moment produced would
be in a clockwise direction. A graphical representation could be seen from fig 12.
Figure 10. Aileron hinge moment coefficient vs
alpha (without tabs)
Figure 11. Aileron hinge moment coefficient vs
alpha (with servo and trim tabs)
Figure 12. Positive aileron deflection(3)

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Shown in fig. 13 and fig. 14 were the effect of hinge moment and stick force due to different
nose balance ratio. According to CASR 23, the maximum stick force that the pilot could produce
had to be 50lbs. From fig. 14, in order for the aircraft to have a maximum stick force of 50lbs, the
nose balance ratio was required to be at least 0.38. This ratio might be more than expected. As
mentioned, a high nose balance ratio would probably cause a disturbance in the flow.
Servo tabs were then installed to the aileron. Servo tab worked in such a way that it would
reduce the pilot stick force by deflecting its surface opposite to the deflection of aileron. It would
help the aircraft to have more pitching moment. The effect of installation of servo tabs and trim
tabs could be seen from fig. 15 and fig. 16.
Figure 13. Aileron hinge moment with varying
nose balance ratio (without tabs)
Figure 14. Stick force required with varying
nose balance ratio (without tabs)

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Fig. 15 and fig. 16 showed the stick force required by the pilot to create a pitching moment
when there were addition of servo tabs and trim tabs respectively. In fig. 15, it clearly proved that
the addition of servo tabs would bring down the nose balance ratio required to produce a
maximum force of 50lbs to 0.27 when the size of the servo tabs was 20% of the total chord. On
the other hand, an aircraft that flew in trim had to have a stick-free condition. This could be done
by reducing the stick force to zero. Trim tab was the surface that would help to fulfill this condition.
As could be seen from fig. 16, trim tabs reduced the stick force to zero with the same nose balance
ratio and tab size. Varying size of horn balance could also affect the ability of the aircraft to
produce pitching moment. The trend could be seen in fig. 17 and fig. 18.
nose balance ratio at different servo tab
geometry
nose balance ratio at different trim tab geometry
(with servo tabs and trim tabs)

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According to fig. 17 and fig. 18, the best horn balance ratio supposed to be in the range of
0.65 to 0.67. By having the horn balance designed as mentioned, the aircraft would likely satisfy
the required CASR 23.
In order to further prove the calculation, different cases which the aircrafts were usually flying
should be studied. These cases include:
- VMCA, where: 𝛿𝑎= 8.9 deg, V=73 KEAS, α= 5 deg, Cha= 0.15(3)
- Tameness, where: 𝛿𝑎= 8.5 deg, V=81.6 KEAS, α= 2.8 deg, Cha= 0.056(3)
- Crosswind capability, where: 𝛿𝑎= 7.2 deg, V=77.3 KEAS, α= -3 deg, Cha= 0.05(3)
- DA trim requirement, where: 𝛿𝑎= 2 deg, V=90 KEAS, α= 4 deg, Cha= 0.073(3)
- Roll rate, where: 𝛿𝑎= 2 deg, V=220 KEAS, α=-1 deg, Cha= 0.03(3)
The aileron hinge moment and stick force for given conditions could be calculated by using
eq. 7 and eq. 8 respectively. Fig. 11 was used to determine the hinge moment coefficient given
its 𝛿𝑎 and α. The results of stick force at particular cases due to installation of servo and trim tabs
could be seen from fig. 19 to fig. 28.
horn balance ratio (with servo tab)
horn balance ratio (with servo and trim tabs)

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geometry (Crosswind capability)
(Crosswind capability)
geometry (DA trim)
(DA trim)

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geometry (Roll rate)
(Roll rate)
geometry (Tameness)
(Tameness)

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Fig. 19 to fig. 28 showed the required stick forces for different cases when the aircrafts were
cruising, with varying nose balance ratio. It was observed that in all cases, the pilot stick force
had always been lower than 50lbs when the nose balance ratio and tab size were 0.27 and 20%
respectively. The results shown from fig. 19 to fig.28 further proved that the nose balance ratio of
0.27 and tab size of 20% would fulfill the CASR requirement.
IV. Conclusion & Recommendation
The result observed from this method prediction showed that different aileron configurations
could result in different amount of hinge moment produced. This happened due to the fact that
hinge moment of the control surface had always been influenced by the flight condition and
geometry of the wing components themselves. By looking at all plots and equations used in this
studies, we would be able to see that different nose and horn balance ratio, servo and trim tab
sizes and also flaperon size would affect the efficiency of the aileron. It was found from fig. 15
and 16 that increasing nose balance ratio and tab size would result in lower stick force needed
from the pilot. However, it was also important to know that high nose balance ratio would tend to
geometry (VMCA)
(VMCA)

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disturb the fluid flow along the airfoil. Servo tab could be considered as one of the vital
components of the wing due to its ability to reduce the hinge moment and increase pitching ability
by deflecting its surface opposite to the direction of aileron deflection. This was done so that the
aircraft would be able to produce more pitching moment with lesser stick force needed.
After going through different possible flaperon sizes, it was found that the best flaperon size
had to be 60 percent of the total chord of the wing. By considering the fluid flowing throughout the
wing, a proper nose balance ratio was also set to be 0.27 with trim and servo tab size of 20% of
the total chord of the wing. As known, CASR required any aircraft to have a maximum stick force
to be 50lbs which could be fulfilled by having such wing configuration. The credibility of the size
of the wing components was also being tested throughout 5 different cases such as VMCA,
tameness, crosswind capability, DA trim and roll rate requirement. On these cases, the result also
showed that the required pilot stick force would be lesser than 50lbs when the same wing
geometry was used.

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Reference:
1. Rachmayanti, Farida. "N219 B12 Geometrical Definition." (2015): n. pag. Web. 19 June
2016.
2. Roskam, J. (1987). Preliminary Calculation of Aerodynamic, Thrust and Power
Characteristics (Vol. 7). Lawrence, KS: The University of Kansas.
3. Dady, M. (2009, August 30). TECHNICAL NOTE FOR PREDICTION HINGE
MOMENT AND AERODYNAMIC BALANCING OF N219-B07 AIRCRAFT.
Retrieved June 19, 2016.
4. Stick Free Characteristics. (n.d.). Retrieved June 22, 2016.
5. Etkin, Bernard and Reid, Lloyd Duff. Dynamics of Flight Stability and Control, 3rd
Edition, John Wiley & Sons, 1996.Cari lagi kalo ada

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Appendix A
AR=9.16;
angle=linspace(-20,20,5);
aoa=linspace(-20,20,5);
coss=-0.784;%*(180/pi);
coshl=-2.757;%*(180/pi);
chab=0.98*(pi/180);
chdb=0.94*(pi/180);
chcl=-0.04;
cladt=0.12;
adtcl=-0.37;
M=0.3; %Mach at steady flight
cham=(chab/(1-M^2)^0.5);%*(pi/180);
cha=-((((AR*cos(coss))/(AR+(2*cos(coss)))))*(cham));
chdm=(chdb/((1-M^2)^0.5));%*(pi/180);
chd0=((cos(coss))*cos(coshl))*((chdm)+((-
0.49).*(cham).*((2*cos(coss))/(AR+(2*cos(coss))))));
chdm30=((cos(coss))*cos(coshl))*((chdm)+((-
chdt=chcl*cladt*adtcl;
chtotal0=(0.0013+(cha.*aoa)+(chd0*0)+(chdt*0));
chtotalm30=(0.0013+(cha.*aoa)+(chdm30*-30)+(chdt*-15));
chtotal01=(0.0013+(cha.*aoa)+(chd0*0));
chtotalm301=(0.0013+(cha.*aoa)+(chdm30*-30));
figure(1)

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plot(angle,chtotalm30)
hold on
hold on
hold on
plot(angle,chtotal0)
hold on
hold on
hold on
hold off
grid on
xlabel('Angle of Attack')
ylabel('Cha')
legend('da=-30','da=-20','da=-10','da=0','da=10','da=20','da=30')
title('Cha vs Angle of Attack with Difference in Deflection Angles of
Aileron')
figure(2)
hold on
hold on
hold on
hold on
hold on
hold on
hold off
grid on
xlabel('Angle of Attack')
ylabel('Cha')
legend('da=-30','da=-20','da=-10','da=0','da=10','da=20','da=30')
title('Cha Without Trim Tab vs Angle of Attack with Differece in Deflection
Angles of Aileron')
%hinge moment calc at different scenarios
AR=9.16;
coss=-0.784;%*(180/pi);
coshl=-2.757;%*(180/pi);
chab=0.98*(pi/180);
chdb=0.94*(pi/180);
chcl=-0.126; %-0.11; %cf/c 67%

24
cladt=0.12;
adtcl01=-0.37;
adtcl015=-0.45;
adtcl02=-0.5;
adtcl025=-0.56;
adtcl03=-0.62;
adtcl035=-0.66;
adtcl04=-0.72;
varycbcf=[0.1 0.15 0.2 0.25 0.3 0.35 0.45];
varychab=[1.1 0.92 0.8 0.64 0.52 0.4 0.16]*(pi/180);
%varychab=[2 1.4 1 0.8 0.7 0.65 0.62]*(pi/180);
varycham=(varychab./(1-M^2)^0.5);%.*(pi/180);
varycha=-((((AR*cos(coss))/(AR+(2*cos(coss)))))*(varycham))*(pi/180);
varychdb=[1 0.82 0.72 0.6 0.44 0.3 0]*(pi/180);
chdt01=chcl*cladt*adtcl01;
varychdm=(varychdb/((1-M^2)^0.5));%*(pi/180);
varychd0=((cos(coss))*cos(coshl))*((varychdm)+((0.75).*(varycham).*((2*cos(co
ss))/(AR+(2*cos(coss))))));
% chdm30=((cos(coss))*cos(coshl))*((chdm)+((-
% chd10=((cos(coss))*cos(coshl))*((chdm)+((-
%chdt=chcl*cladt*adtcl;

25
varychtotal01=(-((0.0013+(varycha.*1)+(varychd0*2))))%+(chdt*2)));
hm0=varychtotal01.*0.5*1.225*(113.2^2)*2*1*0.382;
force=hm0*1.75;
varychtotaltab01=(-((0.0013+(varycha.*-1)+(varychd0*2))+(chdt01*1)));
hm01=varychtotaltab01.*0.5*1.225*(108.1^2)*2*1.096*0.382;
force01=hm01*2.07;
force015=hm015*2.07;
force02=hm02*2.07;
force025=hm025*2.07;
force03=hm03*2.07;
force035=hm035*2.07;
force04=hm04*2.07;
% chtotalm301=(0.0013+(cha.*aoa)+(chdm30*-30));
% chtotal101=(0.0013+(cha.*aoa)+(chd10*10));
figure(1)
plot(varycbcf,hm0)
grid on
title('Hinge moment vs nose balance')
xlabel('cb/cf')
ylabel('Hm(Nm)')
figure(2)
plot(varycbcf,force)
grid on
title('Force vs nose balance')
xlabel('cb/cf')
ylabel('F(lb)')
figure (3)
plot(varycbcf,force01)

26
hold on
hold on
hold on
hold on
hold on
hold on
hold off
grid on
legend('Stab 10%','Stab 15%','Stab 20%','Stab 25%','Stab 30%','Stab
35%','Stab 40%')
xlabel('nose balance')
ylabel('F(lb)')
title('Aileron force due to servo tab effect')
varychtotaltab011=-(0.0013+(varycha.*-1)+(varychd0*2)+(chdt01*1)+(chdt01*1));
varychtotaltab0151=-(0.0013+(varycha.*-
1)+(varychd0*2)+(chdt015*1)+(chdt015*1));
% varychtotaltab011=(-((0.0013+(varycha.*1)+(varychd0*2))+(chdt01*3)));
force011=hm011*2.07;
force0151=hm0151*2.07;
force021=hm021*2.07;
force0251=hm0251*2.07;
force031=hm031*2.07;
force0351=hm0351*2.07;

27
force041=hm041*2.07;
% figure(1)
% plot(varycbcf,hm0)
%
% figure(2)
% plot(varycbcf,force)
% grid on
figure (4)
hold on
hold on
hold on
hold on
hold on
hold on
hold off
grid on
legend('Ttab 10%','Ttab 15%','Ttab 20%','Ttab 25%','Ttab 30%','Ttab
35%','Ttab 40%')
ylabel('F(lb)')
title('Aileron force due to servo tab and trim tab effect')
AR=9.16;
coss=-0.784;%*(180/pi);
coshl=-2.757;%*(180/pi);
chab=0.98*(pi/180);
chdb=0.94*(pi/180);
chcl=-0.126; %-0.11; %cf/c 67%
cladt=0.12;
adtcl01=-0.37;
adtcl015=-0.45;
adtcl02=-0.5;
adtcl025=-0.56;
adtcl03=-0.62;

28
adtcl035=-0.66;
adtcl04=-0.72;
varycbcf=[0.1 0.15 0.2 0.25 0.3 0.35 0.45];
varychab=[1.1 0.92 0.8 0.64 0.52 0.4 0.16]*(pi/180);
%varychab=[2 1.4 1 0.8 0.7 0.65 0.62]*(pi/180);
varycham=(varychab./(1-M^2)^0.5);%.*(pi/180);
varycha=-((((AR*cos(coss))/(AR+(2*cos(coss)))))*(varycham))*(pi/180);
varychdb=[1 0.82 0.72 0.6 0.44 0.3 0]*(pi/180);
varychdm=(varychdb/((1-M^2)^0.5));%*(pi/180);
varychd0=((cos(coss))*cos(coshl))*((varychdm)+((0.49).*(varycham).*((2*cos(co
ss))/(AR+(2*cos(coss))))));
%chdt=chcl*cladt*adtcl;
varychtotal01=(-((0.0013+(varycha.*1)+(varychd0*2))))%+(chdt*2)));
hm0=varychtotal01.*0.5*1.225*(113.2^2)*2*1*0.382;
force=hm0*1.75;
varychtotaltab01=(-((0.0013+(varycha.*1)+(varychd0*2))+(chdt01*1)));

29
force01=hm01*2.07;
force015=hm015*2.07;
force02=hm02*2.07;
force025=hm025*2.07;
force03=hm03*2.07;
force035=hm035*2.07;
force04=hm04*2.07;
figure(1)
plot(varycbcf,hm0)
figure(2)
plot(varycbcf,force)
grid on
figure (3)
hold on
hold on
hold on
hold on
hold on
hold on
hold off
grid on
legend('Stab 10%','Stab 15%','Stab 20%','Stab 25%','Stab 30%','Stab
35%','Stab 40%')

30
ylabel('F(lb)')
title('Aileron force due to servo tab effect')
varychtotaltab011=-(0.0013+(varycha.*1)+(varychd0*2)+(chdt01*1)+(chdt01*1));
varychtotaltab0151=-
(0.0013+(varycha.*1)+(varychd0*2)+(chdt01*1)+(chdt015*1));
force011=hm011*2.07;
force0151=hm0151*2.07;
force021=hm021*2.07;
force0251=hm0251*2.07;
force031=hm031*2.07;
force0351=hm0351*2.07;
force041=hm041*2.07;
% figure(1)
% plot(varycbcf,hm0)
%
% figure(2)
% plot(varycbcf,force)
% grid on

31
figure (4)
hold on
hold on
hold on
hold on
hold on
hold on
hold off
grid on
legend('Ttab 10%','Ttab 15%','Ttab 20%','Ttab 25%','Ttab 30%','Ttab
35%','Ttab 40%')
ylabel('F(lb)')
title('Aileron force due to servo tab and trim tab effect')

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