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Study on Low Reynolds Number Airfoil Design for Micro Air Vehicle (MAV) with Adaptive Wing

Ranggi S. Ramadhan

MSc Aerodynamics and Aerostructures

Department of Mechanical Engineering, University of Sheffield

Abstract

In order to perform efficiently in various working condition, morphing or adaptive wing is now being researched

for Micro aerial vehicle (MAV) application. The purpose of this study is to investigate and obtain the optimum

wing design for MAV at two different flight condition: cruise and loiter. The design includes analysis and

simulation using XFOIL software, and focused on airfoil selection for low Reynolds number application.

Laminar separation bubble and transition point was found and its effect to airfoil performance is discussed.

The result shows that NACA 1203 and 6406 are the optimum airfoil profile for cruise and loiter condition.

I. Introduction

Micro aerial vehicles or MAVs, is often described as

small, lightweight aircraft that is controlled remotely

by operator. It is built for specific mission such as

surveillance or intelligence for both civil and

military purposes. Propelled mostly by electric

motor, MAVs are expected to operate in wide variety

of speed and working environment, therefore

efficient aerodynamic performance is expected [1]

[2] [3]. In order to meet the expected aerodynamic

performance at different operating condition,

morphing or adaptive wing design is proposed for

future MAV development. Morphing or adaptive

wing described as a wing which has capability to

change its shape during flight, through some

actuators. Some of the method like twist morphing

(TM) was already investigated [4].

Meanwhile, due to its small dimension and low

flying speed, MAVs operate in the low Reynolds

regime compared to the larger, manned aircraft. This

somehow bring undesirable characteristics such as

low lift to drag ratio caused by laminar separation

bubbles (LSB) and transition. Laminar separation

bubbles is caused by the inability of the flow to make

transition to turbulent flow on the surface of airfoil

and instead separates before transition. It

characterized by laminar separation, laminar-

turbulent transition and turbulent reattachment. This

separation bubbles become one of the main source

of high drag on low Reynolds number airfoil [5] [6]

[7].

This report presents a study in adaptive MAV wing

design for specific operating condition. The study

includes analytical and numerical method in

deciding the optimum wing platform and profile that

satisfy design requirement.

The numerical method is conducted using XFOIL, a

design and analysis software for subsonic isolated

airfoils [8]. The design work includes selection of

wing aspect ratio and optimum 4-digit NACA

profile for cruise and loiter condition. Although

assumptions and idealizations are made to limit and

simplify the design work, it still gives a good basic

understanding in wing design and the effect of low

Reynolds number regime.

II. Methods

II.1. Problem definition

The purpose of this study is to find the optimum

wing design for MAV at cruise and loiter condition.

Cruise defined as a flight when the MAV fly in its

normal speed, steady with no acceleration and with

no change in altitude. While loiter is also defined as

a constant speed level altitude flight but with lower

velocity. The upcoming wind is assumed to always

parallel in the direction of the flight, and the wind

speed relative to the MAV speed is always zero.

Therefore, in both cruise and loiter condition, lift is

always the same with aircraft weight and thrust is

always the same with drag, as shown in equation (1a)

and (1b)

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Table 1. Design Specification

𝐿 = 𝑊 (1a)

𝑇 = 𝐷 (1b)

Meanwhile Table 1 shows the design specification

of the MAV. It is assumed to fly in sea level

condition with given density and viscosity. It has

cruise speed of 15 m/s and loiter speed of 8 m/s. The

weight is 5 N and has wing area of 0.13 m2. The wing

shape is determined to be rectangular with span

efficiency of 0.9. The MAV is treated as a flying

wing, therefore the effect of other aircraft

component to aerodynamics performance is ignored.

Also, it is assumed that the airfoil profile of the wing,

includes its thickness, maximum camber and camber

position can change for not only cruise or loiter

condition, but also for take-off, climb and landing

condition. However, this study would primarily

discus about the wing design in cruise and loiter

condition. The optimum design would aim the

highest L/D value possible, with minimum total drag

and a consideration in a structural issue.

II.2. XFOIL

XFOIL is an interactive analysis and design software

written by Mark Drela from Massachusetts Institute

of Technology. The first 1.0 version was written in

1986 and has been upgraded and modified for

specific application ever since. For inviscid

formulation, XFOIL use linear-vorticity panel

method. And for the trailing edge base thickness is

modelled with a source panel. While for viscous

formulation, the velocity at each point on the airfoil

surface and wake is obtained from vortex panel

solution with Karman-Tsein correction [8]. This

software is used in this study to obtain optimum

wing profile and analysing the boundary layer

phenomenon over tested airfoils.

II.3. Wing platform optimization

In wing design, the term Aspect Ratio (AR) is

defined by equation (2), which is the square of wing

span divided by wing area. The aspect ratio affects

aerodynamic performance in two opposite way:

increasing value of aspect ratio would decrease

induce drag – which is desirable, but it also reduce

Reynolds number and lift to drag ratio. Since the lift

required by the design specification is constant,

lower lift to drag ratio would mean an increase in

drag.

𝐴𝑅 =𝑏2

𝑆 (2)

In a three-dimensional wing design, an additional

component of induced drag is considered. Induced

drag is an additional component of drag (beside

pressure and friction drag) that arise as a

consequence of a downward velocity component –

so called downwash – reducing the effective angle

of attack. This occurs due to wing-tip vortices

phenomenon, one that can only be observed on finite

wing [9]. Its relation to aspect ratio described by

equation (3).

𝐶𝐷,𝑖 =𝐶𝐿2

𝜋𝑒𝐴𝑅 (3)

Meanwhile, aspect ratio affects Reynolds number by

changing the chord length. With constant wing area

S, a change in wing span would automatically

change the length of chord. And since chord is used

as the effective length to calculate Reynolds number

of flow over airfoil – shown by equation (4), the

change of its value would change the Reynolds

number.

𝑅𝑒 =𝜌∞𝑉∞𝑐

𝜇 (4)

The other consideration on deciding aspect ratio for

aircraft wing is structural issue. The larger the aspect

ratio – thus larger wing span, the more the bending

load experienced at the wing root. Therefore, all the

three parameters namely induce drag, lift to drag

ratio and structural issue become the consideration

of deciding wing platform.

To do the optimization, NACA 2412 and 2812 is

tested on XFOIL using a range of Reynolds number.

The Reynolds number itself is obtained by varying

the aspect ratio. From the test, the total drag of each

aspect ratio variation could be obtained. By also

including the structural issue, the aspect ratio then

can be decided.

II.4. Panel independence study

The underlying principal of XFOIL is panel method,

where a finite number of panel is distributed to

represent the shape of airfoil. This would produce an

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Figure 1. Algorithm of NACA Profile Design

approximation of source panel strength that cause

the body surface become a streamline of the flow.

The approximation can be made more accurate using

more panel numbers, and more closely representing

the source or vortex sheet of continuously varying

strength. The minimum number of panel that

produce accurate result can be obtained using panel

independence study.

The study conducted by simulating NACA 0012 at 5

degree angle of attack with various panel number,

from 10 to 160 panel numbers, with increment of 10.

While the parameter that is being monitored is CL

and CD.

II.5. NACA Profile Selection

To emphasize, the aim of the study is to get the most

efficient airfoil shape for two specific working

condition that is cruise and loiter. With wing area

and aircraft speed has been specified, the CL for

each condition has also been specified following

equation (5).

𝑉∞ = √2𝑊

𝜌∞𝑆𝐶𝐿 (5)

While for certain airfoil shape, certain value of CL

can only be achieved by putting the airfoil at certain

angle of attack. Therefore the airfoil would be

mainly assessed based on the lowest drag at the

given CL. Also, pressure and friction distribution for

several airfoil shape is further examined in order to

get better understanding on the effect of thickness,

camber and camber position to aerodynamic

performance.

Being unrestricted in deciding NACA profile and

with so many options available, algorithm based on

good understanding in aerodynamics is important to

ensure the design process goes efficiently. The idea

of the algorithm is to decide an initial profile, and

then varying its thickness, maximum camber and

camber position consecutively, using the best

parameter from each stage to be used in the next one.

The decision in initial profile was based on the

understanding of aerodynamics, and would

determine the overall result. If other algorithm or

initial design is used, it should be noted that

optimum design obtained would be different. The

algorithm used in this study is shown in Figure 1.

To avoid confusion with XFOIL terms, 2D

coefficient of lift and drag would be stated as CL and

CD instead of cl and cd. Unless being stated otherwise,

the term CL and CD in this study would be considered

for 2D.

II.6. Thrust Estimation

Recalling the equation (1b), the thrust required for

both cruise and loiter condition is equal to the drag

being generated. The wing platform and wing profile

selection would also yield drag value that can be

used for thrust estimation. The drag itself is obtained

using equation 6(a) – (c).

𝐷𝑇𝑜𝑡𝑎𝑙 = 𝐷 + 𝐷𝑖 (6a)

𝐷 = 𝐶𝐷 (1

2𝜌∞𝑉∞

2) (6b)

𝐷𝑖 = 𝐶𝐷,𝑖 (1

2𝜌∞𝑉∞

2) (6c)

III. Result and Discussion

III.1. Wing platform, coefficient of lift and

Reynolds Number

Ten wing platform with different aspect ratio was

tested. 0.3 – 1.2 m wing span was chosen, giving a

range of aspect ratio from 0.7 to 11.1. For NACA

2412 and 2812, effect of aspect ratio to the total drag

is obtained and presented in Figure 2.

Figure 2 shows the total drag for both NACA 2412

and 2812 at various aspect ratio. Generally, it can be

observed that the total drag decrease as aspect ratio

increase for both cruise and loiter condition.

However, closer investigation reveals that a further

increase in aspect ratio above the value of 4

insignificantly decrease the total drag value. This

happened because the decrease in induced drag is

balanced by the increase in parasitic drag for a higher

aspect ratio. This insignificant decrease in total drag

is not beneficial compared to the structural trade-off

that is experienced by the longer-spanned wing.

Therefore, the aspect ratio below 4 is chosen. To be

specific a wing span of 0.6 m, producing aspect ratio

of 2.77 was chosen. A corresponding chord length

and Reynolds number for chosen wing platform is

shown in Table 2. The three-dimensional coefficient

of lift for both cruise and loiter condition, calculated

using equation (5), is also presented in Table 2.

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Figure 2. Total drag for NACA 2412 and NACA

2812 airfoil at various wing aspect ratio

Table 2. Chosen wing platform and corresponding

Reynolds number and coefficient of lift

III.2. Panel independence study

Figure 3(a) shows value of cl and cd for both inviscid

and viscous condition. It can be observed that below

application of 60 panel numbers, the parameters

being monitored show different values for different

panel numbers. Low inviscid cl value of -0.04 was

recorded at the application of 10 panel numbers, and

rose up to 0.013 at 20 panel numbers. The fluctuation

continues until the application of 60 panel numbers,

where it reached a near-zero value. The similar trend

can be found for all other parameters. For the

application of 60 panel numbers or more, the

parameter values did not show any significant

difference. From this finding, it can be inferred that

60 is the minimum number of panels that enables the

simulation to give accurate result. The number of

panels strongly relates to the number of source or

vortex strength that can be approximated over the

airfoil surface. The larger the number, the finer the

distribution of those source/ vortex panel can be

obtained – hence more accurate approximation. For

small number of panels, the distribution over airfoil

would only be captured partially. This might resulted

in a missing information or uncaptured phenomenon

within the result obtained. Prove of this occurrence

is shown in Figure 3(b) and (c).

Figure 3 (a) effects of panel number to cl and cd;

(b) Effect of number of panel on pressure

distribution; (c) skin friction for various number of

panel

Figure 3(b) shows the pressure distribution over

airfoil. The inviscid pressure distribution obtained

from simulation with 80 panels is used as the

reference. It can be seen that the viscous pressure

distribution for simulation using 20 panels –

presented by dash-dot line – shows negligible

separation phenomenon. Meanwhile for application

of 30 and 80 panels, separation observed at around

10% chord length from the leading edge, and

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reattachment is observed at around 30% from the

leading edge. The phenomenon can be more clearly

observed by plotting the coefficient of friction over

the airfoil. As shown by Figure 3(c), application of

20 panel numbers shows no separation with positive

value of coefficient of friction observed along the

airfoil. Meanwhile at application of 30 and 80 panel

numbers, zero coefficient of friction detected from

10% to 30% chord length. As zero coefficient of

friction means that there is no flow that attached and

give friction to the airfoil surface, it can be used as a

good tool to predict flow separation and

reattachment.

Since viscous effects that corresponds to skin

friction and other boundary layer phenomenon are

ignored for the inviscid flow, the calculation for

forces around airfoil for this condition is simpler

compared to viscid one. This should lead to the need

of less panel to get accurate simulation output.

However, the result cannot clearly prove this

assumption, since both inviscid and viscous result

become independence to panel number at relatively

same panel number value.

III.3. NACA profile

Generally, low thickness airfoils is expected to be

thin since increased thickness would hampers the

aerodynamic characteristic, as observed by Okamoto

[5] and Brusov [1]. Therefore, initial thickness for

airfoil design would use a thin airfoil, which is 3%

chord length for cruise condition and 6% chord

length for loiter condition. Cruise condition has a

relatively high Reynolds number and low lift

coefficient compare to loiter condition, so it is

expected to be small cambered fly at small angle of

attack. Therefore, NACA 12xx was chosen to be the

initial design for cruise condition. Meanwhile, loiter

condition has lower Reynolds number and much

higher lift coefficient. Therefore, large cambered

airfoil is expected and NACA 42xx is chosen to be

the initial design.

i. Cruise condition

First in order to investigate the effect of thickness,

aerodynamic characteristics of 5 NACA profiles

namely 1203, 1206, 1209, 1212 and 1221 are

investigated and shown in Figure 4. Figure 4 shows

the drag polar curve that presents drag coefficient,

CD versus the lift coefficient, CL for the 5 NACA

profiles at angle of attack between -1 to 4. From the

graph, it can be seen that NACA 1203 gave lowest

drag coefficient of less than 0.007 for the target CL

of 0.31. It is also observed that the increase in

thickness decrease the aerodynamic performance.

Figure 4. Drag polar for 1% camber 20% camber

position airfoil with various thickness

For the same lift coefficient, the drag coefficient

produced was 0.007, 0.008, 0.0095 and 0.013 for

thickness of 6%, 9% 12% and 21% consecutively.

The relation between thickness and aerodynamic

performance can be further investigated by

observing Figure 5.

Figure 5 compares the pressure coefficient and skin

friction coefficient over airfoil with three different

thickness which are 3%, 12% and 21%. The airfoils

has same camber and camber position, and tested at

same angle of attack. The figure shows that the

thinnest NACA 1203 airfoil experience negligible

separation at the leading edge, and the flow stay

attached along the chord length. The flow is also

laminar at all airfoil surface, shown by the transition

point of 1 at the top and the bottom part of airfoil.

This produce excellent aerodynamic performance.

Meanwhile laminar separation bubble (LSB) was

observed at the upper part of airfoil for 12%-

thickness NACA 1212. It can be seen that the flow

started to separate from the leading edge, experience

transition at around 60% from the chord and then

reattach. The LSB is detected from the viscous

pressure coefficient moves away from the inviscid

pressure coefficient, and the near-zero skin friction.

This separation bubble decrease the aerodynamic

performance of the airfoil. Longer and deeper

separation bubble is observed at the 21%-thickness

NACA 1221 airfoil. It can also be observed that the

separation bubble formed at the upper as well as the

lower part of airfoil. This phenomenon decrease the

aerodynamic performance even further.

In such a low Reynolds number, which become the

case of the study, the separation bubble formed due

to the significant adverse pressure gradient. The

insufficient energy at the flow cannot overcome the

pressure gradient and then separates. At thicker

airfoil, higher adverse pressure gradient is apparent

because of the more curvature surface. Hence in the

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Figure 5. Pressure and skin friction coefficient for NACA 1203, 1212 and 1221

cruise condition, thicker airfoil would likely to form

more separation bubble, which is undesirable.

Therefore, the 3% thickness is chosen for the cruise

condition.

The next step is to find the maximum camber. One

non-cambered and four different cambered airfoils

of 1%, 2%, 3% and 4% camber is tested. The

thickness used was the optimum thickness that is

obtained from previous investigation, which is 3%.

While the camber position is 20% of chord from the

leading edge. The airfoil was tested at a range of

angle of attack and the result is presented in Figure

6.

Figure 6. Drag polar for 3% airfoil thickness with

various camber

Figure 6 shows the drag polar of 5 airfoils at a range

of angle of attack. It is apparent that for the targeted

CL of 0.31, NACA 1203 produced lowest drag

coefficient of nearly 0.007. Meanwhile for higher

camber, higher value of drag was obtained to

produce same amount of targeted lift. The non-

cambered airfoil also give a high value of drag

coefficient for the targeted lift. To investigate the

effect of maximum camber, pressure coefficient

curve and skin friction curve for three different

airfoil is plotted and shown in Figure 7.

Figure 7 shows the pressure and skin friction

coefficient for NACA 0003, 2203 and 3203, all in

their own specific angle of attack that produce lift

coefficient of 0.31. To produce lift coefficient of 0.3,

NACA 0003 needed to set 2.76o of angle of attack.

This value is a rather high angle of attack for such

thin non-cambered airfoil. Therefore, the separation

and transition happened very early at the leading

edge and showed stalling phenomenon. This

occurrence leads to a low lift to drag ratio.

Meanwhile the NACA 2203 produce lift coefficient

of 0.31 at the 1.2o AoA. Both pressure and skin

friction coefficient curve shows that neither

separation bubble nor transition occurred along the

airfoil. This is desirable and produce a good

aerodynamic performance. In the other hand, NACA

3203 produce lift coefficient of 0.31 at a small, 0.223

angle of attack. This small angle of attack at a

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Figure 7. Pressure and skin friction coefficient for NACA 0003, 2203 and 3203

relatively high cambered airfoil induce the transition

to occur at the lower part of the airfoil. As can be

seen from the figure, the transition point for the

lower part of NACA 3203 airfoil is 0.0286 – at the

leading edge. This resulting in poorer L/D value. By

revisiting Figure 6, it is clear that the cambered

airfoils are more suitable to obtain higher CL as it

gave lower drag at higher lift. While for lower CL,

small cambered airfoil is preferable.

Finally, after the optimum thickness and maximum

camber is obtained, optimum camber position was

investigated. Four camber position of 20%, 40%,

60% and 80% of chord length from the leading edge

was tested and the result is presented in Figure 8.

Figure 8. Drag polar of 2% camber 3% thickness

airfoil with various camber position

Figure 8 shows the drag polar for NACA 2203, 2403,

2603 and 2803. It is clearly observed that the further

the camber moves to the trailing edge, the higher the

drag is produced for the targeted lift. From the

pressure and skin friction coefficient graph shown in

Figure 9, it can be seen that the camber position

affects the pressure gradient along the airfoil. When

camber is closer to the leading edge for NACA 2203,

the high pressure gradient is observed at the front

part of the airfoil. The high pressure gradient then

moves backward as the camber position moves

further to the trailing edge. From the investigation, it

can be inferred that the 20% from the leading edge

is the optimum camber position.

The investigation in the effect of thickness, camber

and camber position shows that NACA profile of

1203 is the optimum profile for cruise condition.

ii. Loiter condition

The same approach is used to get the optimum

NACA profile for the loiter condition. To investigate

the effect of thickness, 4% cambered, 20% camber

position airfoil with different thickness are tested

and the result is shown in Figure 10.

Figure 10 shows the drag polar for NACA 4206,

4209, 4212 and 4221. It is vividly shown by the

figure that the increase in thickness deteriorate the

aerodynamic performance of airfoil. To get the same

targeted CL value, thicker airfoil produced higher

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Figure 9. Pressure and skin friction coefficient for NACA 2203, 2603 and 2803

drag coefficient. The effect of thickness is further

investigated by looking at Figure 11, where the

pressure and skin friction coefficient of 6%, 12% and

21% thickness airfoil for the same angle of attack is

plotted. It is apparent that, while all the three airfoils

show the same tendency to produce laminar

separation bubble, thicker airfoil produce higher

skin friction especially near the leading edge.

Moreover, while the separation bubble is followed

by reattachment at NACA 4206, the separation

bubble is followed by a further turbulent separation

especially at NACA 4221. This leads to the lower

L/D value for thicker airfoil. Therefore, the 6% is

chosen to be the optimum thickness.

Figure 10. Drag polar for 4% camber 20% camber

position airfoil with various thickness

Meanwhile effect of camber is investigated by

plotting drag polar of four airfoils with different

camber, as shown in Figure 12. From the figure, it

can be inferred that NACA 4206 and 6206 produce

a similar, lowest drag coefficient. A closer

investigation shows that NACA 6206 produce

slightly lower L/D at the same CL and thus chosen to

be the optimum design. The effect of camber is

closer observed by Figure 13. To produce the same,

relatively high CL of 1.09, small cambered NACA

1206 needs AoA of 25.41o which produce stall and a

very low L/D value. While for the same CL, airfoil

profile with larger camber needs lower AoA. AoA of

6.57o and 4.88o is observed for NACA 4206 and

6206 consecutively. This lower AoA reduce the

adverse pressure gradient that has to be overcame by

the flow, enables the flow to reattach easier and

brought the airfoil away from the stall effect.

Therefore, 6% is chosen to be the optimum camber.

Investigation of the camber position effect to

aerodynamic performance at loiter condition is

shown in Figure 14 and 15. Figure 14 presents the

drag polar of four different airfoils, showing that the

40% chord length from the leading edge yield lowest

L/D among the airfoil being tested. Meanwhile

Figure 15 shows that moving camber position from

20% to 40% chord length move the separation

bubble and transition point away from the leading

edge. Meanwhile, by moving the camber further to

9

Figure 11, Pressure and skin friction coefficient for NACA 4206, 4212 and 4221

Figure 12. Drag polar for 20% camber position 6% thickness airfoil with various camber

80% of chord length form the leading edge,

transition point moves to the leading edge and severe

separation occurred over the airfoil. This resulted in

a poor L/D value.

Finally, the investigation in the effect of thickness,

camber and camber position shows that NACA

profile of 6406 is the optimum profile for loiter

condition.

III.4. Thrust

Using equation (3) to calculate induced drag

coefficient and XFOIL to obtained parasitic drag

coefficient, and using equation 6(a)-(c), the Drag for

cruise and loiter condition can be calculated. The

drag for cruise condition is 0.32 N while drag for

loiter condition is 2.79 N. And by recalling equation

1(b), the calculated drag can also be used to

represent the thrust.

10

Figure 13. Pressure and skin friction coefficient for NACA 1206, 4206 and 6206

Figure 14. Drag polar for 6% camber 6% thickness airfoil with various camber position

Table 3. Final wing design for loiter and cruise condition

11

Figure 15. Pressure and skin friction coefficient for NACA 6206, 6406 and 6806

IV. Conclusion

The optimum wing design of cruise and loiter

condition for Micro-Air-Vehicle (MAV) is obtained.

By considering induced drag and Reynolds number

effect, as well as structural issue, aspect ratio of 2.77

was chosen. For the cruise condition, NACA profile

of 1203 was found to be the optimum design, giving

L/D ratio of 48.43 at angle of attack of 1.85 degree.

While NACA profile of 6406 is obtained as the

optimum design, giving L/D as high as 69.65 at

angle of attack of 3.88 degree. The final design

specification is shown in Table 3.

Generally, airfoil with low thickness is suitable for

low Reynolds number application. This is due to the

lower adverse pressure gradient produced by thinner

airfoil, minimizing the separation and the occurrence

of laminar separation bubble. This result agrees with

other research [1] [5]. Meanwhile, high cambered

airfoils become effective to obtain high value of lift

coefficient. Therefore, higher cambered airfoil is

suitable for loiter condition while lower one is

suitable for cruise condition. In the other hand,

camber position control the distribution of pressure

gradient over the airfoil.

Laminar separation bubble and transition point

become one of the main concern for airfoil flow over

low Reynolds number. Laminar separation bubble

was found in several airfoil design and is proven to

decrease the performance of airfoil. The bubble, the

longer and deeper it becomes, induced an

undesirable drag raise.

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