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Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

TITLE RESEARCH QUESTION APPROACH

Identification of the effects of plain trailing-edge flap deflection on wing properties How are the lift, lift coefficient, zero-lift angle of attack, and stalling angle of attack of a wing with a NACA 2412 airfoil dependent on plain, trailing-edge flap deflection?

An experimental and theoretical approach is taken. The effect of flap deflection on wing lift is determined first from numerical thin-airfoil theory and then from empirical data collected in a low-speed wind tunnel. Results are compared and a conclusion is made in real-world context with uncertainty levels appreciated.

WORD COUNT: 3’999/4’000

AN IB EXTENDED ESSAY IN PHYSICS

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Dedicated to my family, the time with which was foregone in the writing of this essay.

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

The Abstract This is an experimental study considering the change the lift, lift coefficient, zero-lift angle of attack, and stalling angle of attack of a wing with a NACA 2412 airfoil and a plain trailing-edge flap when this flap is deflected. The wing has an aspect ratio of 3.2 and the flap chord to wing chord ratio is 0.36, hence allowing for both large enough increments in the maximum lift to be measured and a small enough error to be made in predicting flap deflection effects with thin airfoil theory (this theory is bad at predicting flap effects at low flap-to-wing-chord ratios). To experimentally test the effect of flap deflection on the lifting characteristics of my wing in real life, a homemade wind tunnel was made and lift data in grams (or the equivalent grams-force) was taken by connecting the wing to a 2 D.P. balance via rods through the tunnel floor. The power plant provided a steady airflow of 4.1 m/s, allowing the wing to create appreciable lift to be collected as data. This data along with aerodynamic formulae and graphical analysis were used to convert raw lift into section lift coefficient and the zero-lift angle of attack values for different flap deflections. This allowed for several data plots to be created which showed that the maximum lift and lift coefficient were directly and positively proportional to flap deflection and that the zero-lift angle of attack was negatively, but also directly, proportional to flap deflection. It was likewise discovered that flap deflection decreases the stall angle of attack, but in so doing it increases the maximum lift achieved before this angle. Compared against textbook data, this showed that a homemade wind tunnel can correctly predict theoretical trends but cannot give accurate experimental values due to design limitations. Word Count: 296

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Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

T ABLE OF C ONTENTS The Abstract ............................................................................................................................................. i Introduction ............................................................................................................................................. 1 A briefing on flight mechanics ................................................................................................................ 1 The airfoil ............................................................................................................................................ 1 Basic forces acting on an airborne body.............................................................................................. 2 The lift equations ................................................................................................................................. 2 Reynolds number................................................................................................................................. 3 Boundary layer theory ......................................................................................................................... 3 Thin airfoil theory ............................................................................................................................... 5 Thin airfoil theory applied to trailing-edge flaps................................................................................. 5 What are plain trailing-edge flaps?.................................................................................................. 6 Applying flaps to a ‘thin airfoil’ ...................................................................................................... 6 Hypothesis ............................................................................................................................................... 7 Physics-based ...................................................................................................................................... 8 Thin-airfoil based ................................................................................................................................ 8 Experimental design & procedure ......................................................................................................... 11 Design................................................................................................................................................ 11 Method .............................................................................................................................................. 12 Safety ................................................................................................................................................. 13 Wind tunnel test results ......................................................................................................................... 13 vs.

plots....................................................................................................................................... 14

vs. vs.

plots .................................................................................................................................... 19 plots .................................................................................................................................. 21

Conclusion on relationship between

and

, , and

.................................................................. 24

Scrutiny ................................................................................................................................................. 24 Of method and apparatus ................................................................................................................... 25 Of wind tunnel ................................................................................................................................... 27 Bibliography .......................................................................................................................................... 29 Appendices ............................................................................................................................................ 31 A ........................................................................................................................................................ 31 B ........................................................................................................................................................ 33 C ........................................................................................................................................................ 35

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 D ........................................................................................................................................................ 37 E ........................................................................................................................................................ 41 F ......................................................................................................................................................... 43 Apparatus diagram ........................................................................................................................ 43 Apparatus photographs .................................................................................................................. 44 G ........................................................................................................................................................ 45 H ........................................................................................................................................................ 47 I.......................................................................................................................................................... 49 J ......................................................................................................................................................... 50 K (Nomenclature) .............................................................................................................................. 52

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

I NTRODUCTION Aerodynamics is the study of the motion of air and of objects through air.1 Interaction with air particles, engineers, and good theories are what airplanes rely on to operate flawlessly. This paper uses thin-airfoil theory and a wind tunnel to investigate one of the most important aspects of a wing: flaps. Flaps provide the lift (and drag) necessary for large airplanes to take off and land in length-constrained spaces. Engineers must know how flaps affect wing lift; with this knowledge, more efficient flaps can be made which will allow airplanes to take off in shorter distances, saving money, energy, and space in building smaller airports in a world where space is becoming limited. I consider the effects of flap deflection on maximum lift, lift coefficient, and stalling and zero-lift angles of attack of a wing with a NACA 2412 airfoil. These properties are major aircraft performance factors, and I will measure them using a home-made wind tunnel whose accuracy I will compare to computational fluid dynamics (CFD) and professional wind tunnels- key tools in aircraft design.

A BRIEFING ON FLIGHT M ECHANICS Background aerodynamic knowledge was required for this paper. Appendix K (Nomenclature) defines the symbols used in this paper.

T HE AIRFOIL The airfoil is a cross-section perpendicular to the wing span. I needed to know about two airfoil properties; the angle of attack, , and the camber line. angle between

is the

and the chord line, and the camber line is constructed from points midway between

upper and lower airfoil surfaces measured perpendicular to the camber line itself. Fig.1 illustrates these:

1

"Aerodynamics Definition." NASA. NASA. Web. 14 July 2011. .

1

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

2

Figure 1 Airfoil section terminology

B ASIC FORCES ACTING O N AN AIRBORNE BODY By Newton’s second law, an object’s motion depends on the forces/moments acting on it: (

)

Four forces act on an airplane: lift, drag, thrust, and weight. Only lift and drag are aerodynamic forces as such forces arise from pressure or viscous shear forces only, and lift equals weight while thrust equals drag in non-accelerated flight.3 Fig.2 shows this:

4

Figure 2 Forces acting on an aircraft in level flight (angles exaggerated)

T HE LIF T EQUA TIONS

2

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 27. Print.

3

Phillips, Warren F. "1.1 Introduction and Notation." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print.

4

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 261. Print.

2

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 Concepts of lift airfoil) whilst

and section lift ̃ exist. ̃ refers to a wing with no wingtips (an infinite wing or a 2D refers to a finite wing; ̃ is hence always greater than

because lift decreases near the

wingtips of a finite wing due to induced drag. In my wind tunnel, wingtips were placed very close to the tunnel walls, so finite affects were minimized, making ̃ more appropriate: ̃

̃ So ̃ is: ̃

̃

R EYNOLDS NUMBER The Reynolds number is a ratio of the magnitudes of pressure to viscous aerodynamic forces (a higher value indicates the dominance of pressure forces):

My wing operates at low

because of low

and short chord length, so viscous forces will be

significant. Thin airfoil theory only analyzes pressure forces, limiting the accuracy of its predictions for my experiment.

B OUNDARY LAYER THEORY This theory states that viscous effects for flow over a wing at low

and high

are confined to a thin

layer around the wing’s surface. Outside this layer, viscous forces are insignificant. Fig.3 shows this:

3

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

5

Figure 3 Boundary layer flow over an airfoil To note:

Pressure forces dominate at high

Inviscid (pressure-only) flow analysis is accurate for high

Boundary layer separation occurs at high

. flow.

(Fig.4).

6

Figure 4 Wake formation behind an airfoil beyond the critical angle of attack

Fig.4 is referred to as a stall, which is reached after a near-linear increase in ̃ as in Fig.5:

5

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 14. Print.

6

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 15. Print.

4

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

3 2

4

1

7

1.

Figure 5 Lift curve of NACA 0012 airfoil ̃ increases as a linear function of .

2. Pressure build-up on top of the wing eventually causes partial boundary layer separation, flattening the slope. 3. At “maximum” , a Fig.4 wake occurs. Airfoil geometry influences the sharpness of this “cusp”. 4. Lift rapidly decreases. Beyond

, lift becomes independent of airfoil shape.8

T HIN AIRFOIL THEORY The thickness of an airfoil with maximum thickness

of chord length has little effect on the

pressure forces acting on it. Thin airfoil theory uses this to simplify such an airfoil to a thin filament (Fig.7, Appendix G).

T HIN AIRFOIL THEORY A PPLIED TO TRAILING - EDGE FLAPS Deflection of a plain flap changes the wing camber line, and the resulting changes in aerodynamic characteristics may be calculated from thin airfoil theory assuming zero flow separation.

7

"AeroCFD Operating Instructions." AeroRocket Simulation Software for Rockets and Airplanes. Web. 20 Nov. 2011. . 8

Phillips, Warren F. "1.4 Inviscid Aerodynamics." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print.

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Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

W H AT

AR E P L AI N TR AI L I N G - E D G E F L A P S ?

Some aft portion of an airfoil is hinged to make a plain trailing-edge flap (Fig.6); rotating it about the hinge axis produces a flap-deflection angle

(Fig.7). A downward deflection increases camber, so is

considered positive. 9

Figure 6 An airfoil section with a deflected flap

A P P L YI N G For small

FL AP S T O A ‘ TH I N AI R F OI L ’

and , thin airfoil theory can predict the effects of flap deflection on lift. Development of

below-given equations is in Appendix H. Fig.7 shows the geometric meaning of terms used in subsequent equations:

9

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 39. Print.

6

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 10

Figure 7 Thin airfoil flap approximation Flap chord fraction is: (

)

Ideal section flap effectiveness is:

Lift coefficient for an airfoil with a plain flap is: ̃ (

)

̃

[

( )

]

is section flap effectiveness (accuracy evaluated in Appendix B):

and

are the section flap hinge efficiency and deflection efficiency (Appendix A).

Using above formulae, one deduces ̃ , then ̃ from ̃

̃

, and

from the lift-curve x-

intercept.

H YPOTHESIS

10

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 40. Print.

7

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

P HYSICS - BASED In a positive plain flap deflection, airfoil camber is increased so air over the top surface has “less space” to travel in than on the bottom surface. From the Law of Continuity:

Hence, decreased cross-sectional area Bernoulli’s Law as dynamic pressure

Lower

will increase airspeed

from

increases:

on top increases lift so a positive correlation with

Lift is a multiple of lift coefficient; ̃ and decrease for positive

and decrease static pressure

should exist.

should also be in positive correlation.

should

as extra lift will have to be suppressed with more negative angles of attack;

there should be a negative correlation between

and .

T HIN - AIRFOIL BASED A spreadsheet (Appendix D) is created using thin airfoil equations to simulate the effect of

on

,

̃ , and ̃ . Results:

8

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Calculated L versus α for various δ 400.0

300.0

200.0

-10° -5°

100.0 L (/gf)

0° 5° 10° 0.0

-20

-15

-10

-5

0

5

10

15

20

25

15° 20° 25°

-100.0

-200.0

-300.0

α (/°)

9

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Calculated CL versus α for various δ 4.0

3.0

2.0 CL (/dimensionless)

-10°

-20

-5° 1.0

0° 5° 10°

0.0 -15

-10

-5

0

5

10

15

20

25

15° 20°

25°

-1.0

-2.0

-3.0

α (/°)

αL0 vs. δ plot 4

2 0

αL0 (/°)

-15

-10

-5

-2

0

5

10

15

20

25

30

-4 -6

Thin airfoil theory

-8 -10 -12 -14 -16

δ (/°)

10

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 Physics-based reasoning was correct- positive

increases lift/lift coefficient and decreases

. This is

an accepted textbook fact, so what I am looking for is the accuracy to which my wind tunnel will match these predictions. NB: thin airfoil theory ignores stall, so I will be able to determine the effect of

on the stall angle of

attack only from wind tunnel tests. Note that lift coefficients greater than 3.0 cannot be achieved on a NACA 2412 airfoil with a plain flap, and high-end coefficients of 2.0 are unlikely to be recorded in my limited wind tunnel. The accuracy of thin airfoil values is hence dubious, but the demonstrated relationship may not be.

E XPERIMENTAL DESIGN & PROCEDURE D ESIGN A 3m home-made wind tunnel with a 0.30mX0.30mX0.30m test section is used. A ProTronik Pro72210 electric motor spinning a 0.254mX0.119m propeller blows air through the tunnel at an average speed of 4.1 ms-1. A NACA 2412 airfoil (Fig.8) is used for the wing; it’s 12% of chord maximum thickness makes it applicable for thin airfoil approximation. The wing is rectangular with 0.300m span and 0.095m chord; the aspect ratio is 3.2. It is made from Styrofoam enclosed in plywood and heat-shrink plastic to reduce friction drag; hinged rods extend through the tunnel floor from its ideal quarter-chord aerodynamic center to a 2 D.P. balance measuring wing mass. A steel rod is hinged to the wing to seamlessly control . An acrylic cover encloses the test section to prevent flow leakage. The wing is mounted at 0.15m above the tunnel floor, almost touching the tunnel sides with the wingtips to reduce effects of finite wingspan.

11

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

11

Figure 8 NACA 2412 airfoil A plain flap is hinged at the trailing edge such that the

ratio is 0.36c below which thin-airfoil

theory produces high error (Appendix B) and above which only marginal

increase is observed12.

Flap deflection is controlled manually. A flow straightener positioned before the test section minimizes the spin the rotating propeller gives to the airflow. Appendix E shows an apparatus diagram.

M ETHOD Independent variable: flap deflection

(/°).

Dependent variables: lift ̃ (/gf13). The method’s aim is to provide a way of collecting lift data accurately (to be converted later to ̃ , , and stall angle

parameters). To collect lift data in /gf:

1. Introduce a 2 D.P. balance underneath the wind tunnel and rest on it an MDF base attached to the wing via rods through the tunnel floor. a. Make sure the balance is zeroed prior to step 1.

11

Photograph. UIUC Airfoil Coordinates Database. Web. 20 Nov. 2011. . 12

Ira H. Abott, Alber E. Von Doenhoff. Theory of Wing Sections. United States: McGraw-Hill Book Company, Inc., 1959. 13

Grams-force (equivalent to grams).

12

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 2. The lift force is to be tested in grams for a range of -10°-25° for

and -15°-20° for , both in

5° increments, so construct an appropriate table/spreadsheet in Excel. 3. Enter an equation “=massbefore-massafter” in the cell for the appropriate

and

condition,

where the massbefore value is the wing mass prior to turning on the fan. 4. First test all positive , so begin by adjusting the wing to 0° alpha and -10° delta. Hence, fill in for massbefore. a. Adjust

by adjusting the wing chord in reference to a protractor mounted in the test

section centered at the wing’s pivot point. b. Adjust

manually with another protractor.

5. Turn on the engine to full throttle and fill in for massafter, completing the equation for the appropriate spreadsheet cell. a. Turn off the engine to save battery. 6. Repeat steps 3-5 for all positive alpha 0°-20° and delta -10°-25°. a. Keep controlled variables constant (Appendix J). 7. Flip the protractor measuring

to repeat steps 3-5 for the negative alpha range, also in 5°

increments. 8. Having taken all raw lift measurements, Excel makes it easy to translate them into

,

,

and ̃ values from graphical analysis and equations in the theoretical section of this paper. 9. Clear up. Process data. Draw a conclusion/evaluation.

S AFETY The fan spins at over 6000 RPM so presents a potential hazard. A fine chicken wire mesh installed at the fan duct prevented accidental contact with the fan’s plane of rotation.

W IND TUNNEL TEST RESU LTS Appendix E presents raw/processed data tables. Notice the absence of error bars due to only one trial of data being collected; collecting more trials to enable error bar calculation is a future improvement. 13

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

̃

VS .

PLOTS

Empirical lift curves for -10°-25° :

L versus α for various δ 60

50

40

30 -10° -5° 20 L (/gf)

0° 5° 10°

10

15° 20° 0 -20

-15

-10

-5

25° 0

5

10

15

20

25

-10

-20

-30

α (/°)

The lift curves follow standard lift curve form. A linear part for small

exists where lift increase is

linear; the curves then level off and the slope becomes negative as the wing stalls at high . This is

14

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 expected from boundary layer theory as the boundary layer separates from the upper surface beyond the stall angle. For 0° , stall occurs at 15°

14.

There was evident friction in my data collection mechanism; as a result, my lift data is lower than the thin airfoil theory predictions, for which the lift slopes are:

Calculated L versus α for various δ 400.0

300.0

200.0 -10° -5° 100.0 L (/gf)

0° 5° 10°

0.0 -20

-15

-10

-5

0

5

10

15

20

25

15° 20° 25°

-100.0

-200.0

-300.0

α (/°)

Note, however, that thin airfoil theory ignores wing stall, in which case theoretical positive lift increments beyond 15°

would be unachievable even in a 100% accurate wind tunnel experiment.

Experimental and theoretical lift slopes show that positive flap deflections translate the =0° lift curve vertically upwards, and downwards for negative flap deflections. Therefore, even though the 14

Evaluation check: the stall angle has a ± few degrees uncertainty as

was taken at 5° intervals.

15

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 magnitude my experimental lift values are below theoretical results, the upward shift of the lift slope is definitely correct as it is backed by both theory and experiment. Judging from data for small , this horizontal translation is almost constant each time15. As proof, one graphs

against

(in degrees):

Lmax vs. δ 70 60

Lmax (/gf)

50 40 Wind tunnel data

30

Linear (Wind tunnel data) 20 10 0 -20

-10

0

10

20

30

δ (/°)

The average linear best-fit shows what the theoretical variation of

could be which, from

inspection of Fig. 9, is most likely the case.

15

Discrepancies at larger alpha may be caused by increasing friction between wing rods and tunnel floor due to higher lift and drag forces

16

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 𝛼 decreases linearly with 𝛿

Notice the very consistent shift upwards of the lift curves with 𝛿.

16

Figure 9 Typical trend for a NACA 66(215)-216 airfoil with 0.20c plain flap My data also shows that the angle of maximum lift coefficient generally decreases with positive flap deflection- this is a trend likewise demonstrated by Fig. 9. Plotting change in ̃

angle,

, versus

:

16

Photograph. Theory of Wing Sections. United States: McGraw-Hill Book, 1959. 195. Print.

17

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

α0 vs. δ plot 18 16 14

12 α0 (/°)

10 Wind tunnel data

8

Linear (Wind tunnel data)

6 4 2 0 -20

-10

0

10

20

30

δ (/°)

Since I was measuring lift data for 5°

increments, I could not capture the gradual decrease in

hence a linear trend line was plotted which shows the likely change in

;

as hypothesized by Fig. 9.

Note from Fig. 10 that the accurate stall angle for the NACA 2412 airfoil is in fact around 14°-16°, which shows that my collected data is roundabout accurate in terms of stall angle at 0° . Hence,

increases the maximum lift of a wing as shown by the positive correlation between

and ̃

. Additionally, there is negative correlation between

and

.

18

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

17

Figure 10 Lift slope for the NACA 2412 airfoil (𝛿=0°)

̃

VS .

PLOTS

A ̃ plot was obtained from its equation in the introduction:

17

Photograph. Theory of Wing Sections. United States: McGraw-Hill Book, 1959. 478. Print.

19

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

CL versus α for various δ 0.7

0.6

0.5

0.4 -10° CL (/dimensionless)

0.3

-5° 0° 5°

0.2

10° 15°

0.1

20° 25°

0.0 -20

-15

-10

-5

0

5

10

15

20

25

-0.1

-0.2

-0.3

α (/°)

The slope of the linear section of graphs above is used to compare lift curves; a steeper linear part suggests that a wing creates more lift per alpha. The discrepancy in lift slopes for =0° between my results and those from NACA (Fig. 10) (their slope: 0.105 deg-1, mine: 0.024 deg-1) may be attributed to friction in my data collection mechanism which would impeded lift increase by friction factor

.

Notice that ̃ is a multiple of ̃ from the section lift equation, so all analysis and evaluation from the previous section applies and will not be repeated here. My experiment has also shown the following relationship between

and the flap deflection

(in

degrees): 20

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

ΔCLmax vs. δ 0.8

ΔCLmax (/dimensionless)

0.7 0.6 0.5 0.4

Wind tunnel data

0.3

Linear (Wind tunnel data)

0.2 0.1 0.0

-20

-10

0

10

20

30

δ (/°)

increases the maximum lift coefficient as shown by the positive correlation between ̃

and

. VS .

PLOTS

My data confirms the hypothesized negative correlation between Comparing wind tunnel data to thin airfoil predictions for Flap deflection (/°)

and

.

and graphing:

αL0 (/°) Empirical

αL0 (/°) Theory

-10

2

3

-5

0

1

0

-2

-2

5

-4

-5-

10

-6

-7

15

-7

-10

20

-19

-12

25

N/A

-15

21

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

αL0 vs. δ plot 5

0 -15

-10

-5

0

5

10

15

20

25

30

αL0 (/°)

-5

Wind tunnel data

-10

Thin airfoil theory

-15

-20

-25

δ (/°)

22

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Linear fit lines calculated with Vernier LoggerPro®

An outlier (ignored for linear fit)

23

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 The theoretical

vs.

slope (=-0.517) appears more negative than the experimental slope (=-0.371).

Notice that thin airfoil theory overestimates equals experimental

for

for negative

and underestimates for positive , and

. This may be due to the theory’s neglect for viscous effects which

perhaps increase with flap deflection due to higher drag. There is a large jump in

between the 15°-20° deflections, and no data for =25°. This is because

my lift curves flatten for negative alpha of large . As higher

increases lift/drag, the rods connecting

the wing to the 2D.P. balance would rub more against their tunnel floor holes, preventing seamless lift force transmission- producing the “leveling off” effect. Thus at large

the extrapolated

value

appears unnaturally low, creating the jump seen above. My results should not be a benchmark for the theory or the theory for my results- my tunnel lacks accuracy due to friction in the data collection mechanism whereas thin airfoil theory wrongfully ignores viscous effects. The values from both are therefore dubious in magnitude, but it is certain that there is a negative correlation between and .

C ONCLUSION ON RELATIO NSHIP BETWEEN

AND

̃ , ̃ , AND

True to my hypothesis, there exists a positive correlation between ̃ correlation between ̃ correlation between

and , a negative correlation between

and , a positive and , and a negative

and . It is of great interest for the engineer and the pilot to know that the

stall angle of attack decreases linearly with positive flap deflection; as a result, it is crucial that the airplane takes off and lands at lower

than usual so as to avoid a stall and a subsequent crash. For a

further investigation in flap deflection effects on aerodynamic properties, I should investigate drag. I predict there would be a proportional rise in the section drag and drag coefficients with increased flap deflection as flow separation and frontal area facing the free stream airflow would increase.

S CRUTINY

24

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

O F METHOD AND APPARATUS The Reynolds number in my experiment was

. This is smaller by 2 orders of magnitude from

the values used in for Fig. 1018. Notice that the lowest comparable19 ̃ 10 was achieved under the lowest

of

value from graph (ο) in Fig.

. The small magnitudes of my ̃ may therefore be

explained by my lower Reynolds number. I may increase my ̃ values by raising

through

increasing airspeed, the chord of the wing, or the fluid viscosity by using something like water (although this is unrealistic for my tunnel). These improvements are questionable in their usefulness as I am merely proving a trend; however, engineers designing planes like the Airbus A380 will need accurate values. The test chamber I used also prevented me from achieving entirely accurate data. From a forum about my tunnel: “Y O U ’ R E … G O I N G T O F I N D T H A T W I T H A 12 X 12 I N C H T E S T A R E A … Y O U ' R E G O I N G TO SUFFER INTERFERENCE FROM THE WAL LS, BOTTOM AND TOP OF THE TEST AREA WITH AIRFOILS IN THE

3 TO 4 INCH CHORD RANGE… IN FULL SIZE WIND

TUNNELS… THE MODELS BEING TES TED ARE TYPICALLY LESS THAN O F T H E C R O S S S E C T I O N O F T H E T E S T A R E A .”

1/10 T H E S I Z E

20

Compression of airflow and wingtip vortices has thus likely offset the accuracy of my results. To improve, I would need to reduce wing size to satisfy above conditions (in which case wingtip vortices would be present), and/or increase the size of the test section (this is not feasible as my tunnel is stationed in school).

18

Fig. 10 is not my own data.

19

The shallowest curve (Δ) is for a rougher, incomparable wing section.

20

BMatthews. RC Universe. s.d. 19 July 2011 .

25

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 One of the largest shortcomings was friction in the data collection mechanism of wing rods against tunnel floor and the wing against the acrylic container in trying to reduce wingtip effects21. The wing rods also had turbulent circular cross-sections; they could be reshaped into symmetric airfoils such as the NACA 0012. The steel rod for changing

was also circular. To avoid this, one could buy

university-grade apparatus, but a more feasible solution may be to implement simple harmonic motion (Appendix I). The accuracy of

and

used, and

was measured in 5° increments, this presented over 20% uncertainty in the

and

measurement could also be improved. As a protractor of 1° uncertainty was

readings! More accurate methods of measuring these variables are implemented in university-grade apparatus in attaching the wing to a device which sets it at an accurate angle while measuring the forces acting on the wing, such as in Fig. 11. 22

Figure 11 A three-component balance designed for use with the AF100 Subsonic Wind Tunnel.

Thin airfoil theory, as previously mentioned, is also worth evaluating. This theory is a tremendous simplification which allows quick performance predictions for aircraft operating at high operated at low

. My wing

so the considerable flow separation and viscous forces acting on it were ignored by

this theory! Hence whereas both empirical and theoretical results agreed on the trend between ̃ and , they rarely agreed on the magnitudes of these values. Thin airfoil theory also ignores stall- an

21

This means reducing wingtip vortices to make the section lift coefficient applicable

22

TecQuipment. s.d. 19 July 2011 .

26

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 important performance factor- so could not predict factors like factors such as separation over my wing at low

. The turbulent flow

also explains the relative irregularity of my data compared to the

linearity of thin airfoil theory that assumes no flow separation.

O F WIND TUNNEL Found through this paper are textbook facts. Presented alone, these give limited value to the extended essay as flap deflection effects on lift are common engineering knowledge. My essay goes beyond information in such books as it evaluates a homemade wind tunnel’s abilities to predict a known aerodynamic relationship. The good. Lift data collected in a homemade wind tunnel enable an engineer to extrapolate results to a wide range of performance features- lift coefficient, maximum lift alpha, effect of zero-lift alpha, etc. These relationships have been compared against recognized sources in this essay and all were correct. An engineer seeking experimental evidence from a wind tunnel will also find these trends; he/she will also have more time than I did and, by collecting data for more alpha and perhaps buying a more powerful engine to increase

, he/she will make patterns in this essay more refined (such as for

)

and thus get better results than I did. The bad. A wind tunnel’s job is to show both trends and values of correct/accurate magnitude. In designing aircraft, it is of little use to an engineer to merely know the trend- he/she must also know the value, such as the maximum lift coefficient. He/she may design a failed aircraft thinking

is 0.7

from an inaccurate homemade wind tunnel test when it is in fact 1.4. As a result, CFD23 methods will be much more useful as they will reveal both patterns and correct values. What makes wind tunnels still useful is their ability to predict what CFD cannot- a wind tunnel must hence be more accurate than a computer code. In the case of my homemade wind tunnel, even though it reveals the trends, its construction is painstaking and will not pay off as its accuracy will be inferior

23

CFD: Computational Fluid Dynamics.

27

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 to that of computer simulation. In my case, CFD will ultimately be both faster and more accurate than a wind tunnel- and this is a topic for a whole another extended essay. Nevertheless, the data achieved in my tunnel enabled me to draw conclusions consistent with those achieved in much more expensive, professional-grade aerodynamic testing facilities. To what extent can a homemade wind tunnel predict the effect of

on wing performance? To the extent of trends, not

of correct values; as a result, what I found is that my wind tunnel enabled me to find the trends I was looking for, and they were correct trends. Never mind that I did not get accurate actual magnitudes of ̃ or ̃ - my wind tunnel enabled me to construct an experimentally-supported argument, and that was its aim. As for an engineer, he/she should seek more elaborate testing facilities and CFD methods to fulfill his/her needs. Word Count: 3’999/4’000

28

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

B IBLIOGRAPHY Internet: "Aerodynamics Definition." NASA. NASA. Web. 14 July 2011. . BMatthews. RC Universe. s.d. 19 July 2011 . Books: Phillips, Warren F. "1.1 Introduction and Notation." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print. Phillips, Warren F. "1.4 Inviscid Aerodynamics." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print. Phillips, Warren F. "1.6 Incompressible Flow over Airfoils." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print. Ira H. Abott, Alber E. Von Doenhoff. Theory of Wing Sections. United States: McGraw-Hill Book Company, Inc., 1959. Video/audio/photo: TecQuipment. s.d. 19 July 2011 . Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 27. Print. Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 261. Print. Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 14. Print. Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 15. Print.

29

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 "AeroCFD Operating Instructions." AeroRocket Simulation Software for Rockets and Airplanes. Web. 20 Nov. 2011. . Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 39. Print. Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 40. Print. Photograph. Theory of Wing Sections. United States: McGraw-Hill Book, 1959. 195. Print. Photograph. Theory of Wing Sections. United States: McGraw-Hill Book, 1959. 478. Print. Database photos : Photograph. UIUC Airfoil Coordinates Database. Web. 20 Nov. 2011. .

30

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

A PPENDICES A Section flap hinge efficiency, section flap effectiveness,

, and deflection efficiency,

, are used in the equation for calculating

:

The values for these parameters are deduced from the following graphs:

Figure A.1 Section flap hinge efficiency for sealed trailing-edge flaps. For unsealed flaps (as in my case) these values should be reduced by 20%.

31

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Figure A.2 Section flap deflection efficiency for sealed trailing-edge flaps. For deflections less than 10°, a deflection efficiency of 1.0 should be used.

32

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

B As seen in Fig. B.1, the section flap effectiveness predicted by thin airfoil theory correlates well to the more complex vortex panel method which takes thickness into account (this method is beyond the scope of this text), but overestimates the actually flap effectiveness calculated from experiment (Fig. B.1 is not my own data).

Figure B.1 Section flap effectiveness compared amongst thin airfoil theory, vortex panel method, and experimental data. As we can see, thin airfoil theory always overestimates actual section flap effectiveness. This is because, in reality, the hinge mechanism about the flap causes local boundary layer separation and flow leakage from the high-pressure bottom surface to the lower-pressure top surface, and this causes the section flap effectiveness to reduce as it is a factor of the section flap hinge efficiency

as in

. In addition, at deflections greater than 10°, error associated with the ideal section flap

33

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 effectiveness for

becomes significant, resulting in the implementation of the factor

in the equation

whose value is calculated from Appendix A.

From Fig. B.1 we see that for a flap chord fraction like mine of about 0.36, the discrepancy in theoretical and experimental results is only about 7%, whereas for smaller flap chord fractions of about 0.1 the error rises to almost 25%. As a result, a flap chord fraction like mine is a good choice for the application of thin airfoil theory as it reaches a good compromise which allows for a small enough error yet provides large enough maximum section lift coefficient increments to reduce percentage error in data as per Abbott and Doenhoff24 and yet does not dominate too much of the airfoil geometry by the flap.

24

Ira H. Abott, Alber E. Von Doenhoff. Theory of Wing Sections. United States: McGraw-Hill Book Company, Inc., 1959.

34

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

C As was mentioned in the main body of the text, thin airfoil theory is a method belonging to a field of inviscid aerodynamics that ignores viscous effects on the forces acting on airborne bodies. Thin airfoil theory is in good agreement with experimental data for low speeds and small

for airfoils

of thickness

View more...
TITLE RESEARCH QUESTION APPROACH

Identification of the effects of plain trailing-edge flap deflection on wing properties How are the lift, lift coefficient, zero-lift angle of attack, and stalling angle of attack of a wing with a NACA 2412 airfoil dependent on plain, trailing-edge flap deflection?

An experimental and theoretical approach is taken. The effect of flap deflection on wing lift is determined first from numerical thin-airfoil theory and then from empirical data collected in a low-speed wind tunnel. Results are compared and a conclusion is made in real-world context with uncertainty levels appreciated.

WORD COUNT: 3’999/4’000

AN IB EXTENDED ESSAY IN PHYSICS

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Dedicated to my family, the time with which was foregone in the writing of this essay.

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

The Abstract This is an experimental study considering the change the lift, lift coefficient, zero-lift angle of attack, and stalling angle of attack of a wing with a NACA 2412 airfoil and a plain trailing-edge flap when this flap is deflected. The wing has an aspect ratio of 3.2 and the flap chord to wing chord ratio is 0.36, hence allowing for both large enough increments in the maximum lift to be measured and a small enough error to be made in predicting flap deflection effects with thin airfoil theory (this theory is bad at predicting flap effects at low flap-to-wing-chord ratios). To experimentally test the effect of flap deflection on the lifting characteristics of my wing in real life, a homemade wind tunnel was made and lift data in grams (or the equivalent grams-force) was taken by connecting the wing to a 2 D.P. balance via rods through the tunnel floor. The power plant provided a steady airflow of 4.1 m/s, allowing the wing to create appreciable lift to be collected as data. This data along with aerodynamic formulae and graphical analysis were used to convert raw lift into section lift coefficient and the zero-lift angle of attack values for different flap deflections. This allowed for several data plots to be created which showed that the maximum lift and lift coefficient were directly and positively proportional to flap deflection and that the zero-lift angle of attack was negatively, but also directly, proportional to flap deflection. It was likewise discovered that flap deflection decreases the stall angle of attack, but in so doing it increases the maximum lift achieved before this angle. Compared against textbook data, this showed that a homemade wind tunnel can correctly predict theoretical trends but cannot give accurate experimental values due to design limitations. Word Count: 296

i

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

T ABLE OF C ONTENTS The Abstract ............................................................................................................................................. i Introduction ............................................................................................................................................. 1 A briefing on flight mechanics ................................................................................................................ 1 The airfoil ............................................................................................................................................ 1 Basic forces acting on an airborne body.............................................................................................. 2 The lift equations ................................................................................................................................. 2 Reynolds number................................................................................................................................. 3 Boundary layer theory ......................................................................................................................... 3 Thin airfoil theory ............................................................................................................................... 5 Thin airfoil theory applied to trailing-edge flaps................................................................................. 5 What are plain trailing-edge flaps?.................................................................................................. 6 Applying flaps to a ‘thin airfoil’ ...................................................................................................... 6 Hypothesis ............................................................................................................................................... 7 Physics-based ...................................................................................................................................... 8 Thin-airfoil based ................................................................................................................................ 8 Experimental design & procedure ......................................................................................................... 11 Design................................................................................................................................................ 11 Method .............................................................................................................................................. 12 Safety ................................................................................................................................................. 13 Wind tunnel test results ......................................................................................................................... 13 vs.

plots....................................................................................................................................... 14

vs. vs.

plots .................................................................................................................................... 19 plots .................................................................................................................................. 21

Conclusion on relationship between

and

, , and

.................................................................. 24

Scrutiny ................................................................................................................................................. 24 Of method and apparatus ................................................................................................................... 25 Of wind tunnel ................................................................................................................................... 27 Bibliography .......................................................................................................................................... 29 Appendices ............................................................................................................................................ 31 A ........................................................................................................................................................ 31 B ........................................................................................................................................................ 33 C ........................................................................................................................................................ 35

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 D ........................................................................................................................................................ 37 E ........................................................................................................................................................ 41 F ......................................................................................................................................................... 43 Apparatus diagram ........................................................................................................................ 43 Apparatus photographs .................................................................................................................. 44 G ........................................................................................................................................................ 45 H ........................................................................................................................................................ 47 I.......................................................................................................................................................... 49 J ......................................................................................................................................................... 50 K (Nomenclature) .............................................................................................................................. 52

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

I NTRODUCTION Aerodynamics is the study of the motion of air and of objects through air.1 Interaction with air particles, engineers, and good theories are what airplanes rely on to operate flawlessly. This paper uses thin-airfoil theory and a wind tunnel to investigate one of the most important aspects of a wing: flaps. Flaps provide the lift (and drag) necessary for large airplanes to take off and land in length-constrained spaces. Engineers must know how flaps affect wing lift; with this knowledge, more efficient flaps can be made which will allow airplanes to take off in shorter distances, saving money, energy, and space in building smaller airports in a world where space is becoming limited. I consider the effects of flap deflection on maximum lift, lift coefficient, and stalling and zero-lift angles of attack of a wing with a NACA 2412 airfoil. These properties are major aircraft performance factors, and I will measure them using a home-made wind tunnel whose accuracy I will compare to computational fluid dynamics (CFD) and professional wind tunnels- key tools in aircraft design.

A BRIEFING ON FLIGHT M ECHANICS Background aerodynamic knowledge was required for this paper. Appendix K (Nomenclature) defines the symbols used in this paper.

T HE AIRFOIL The airfoil is a cross-section perpendicular to the wing span. I needed to know about two airfoil properties; the angle of attack, , and the camber line. angle between

is the

and the chord line, and the camber line is constructed from points midway between

upper and lower airfoil surfaces measured perpendicular to the camber line itself. Fig.1 illustrates these:

1

"Aerodynamics Definition." NASA. NASA. Web. 14 July 2011. .

1

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

2

Figure 1 Airfoil section terminology

B ASIC FORCES ACTING O N AN AIRBORNE BODY By Newton’s second law, an object’s motion depends on the forces/moments acting on it: (

)

Four forces act on an airplane: lift, drag, thrust, and weight. Only lift and drag are aerodynamic forces as such forces arise from pressure or viscous shear forces only, and lift equals weight while thrust equals drag in non-accelerated flight.3 Fig.2 shows this:

4

Figure 2 Forces acting on an aircraft in level flight (angles exaggerated)

T HE LIF T EQUA TIONS

2

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 27. Print.

3

Phillips, Warren F. "1.1 Introduction and Notation." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print.

4

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 261. Print.

2

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 Concepts of lift airfoil) whilst

and section lift ̃ exist. ̃ refers to a wing with no wingtips (an infinite wing or a 2D refers to a finite wing; ̃ is hence always greater than

because lift decreases near the

wingtips of a finite wing due to induced drag. In my wind tunnel, wingtips were placed very close to the tunnel walls, so finite affects were minimized, making ̃ more appropriate: ̃

̃ So ̃ is: ̃

̃

R EYNOLDS NUMBER The Reynolds number is a ratio of the magnitudes of pressure to viscous aerodynamic forces (a higher value indicates the dominance of pressure forces):

My wing operates at low

because of low

and short chord length, so viscous forces will be

significant. Thin airfoil theory only analyzes pressure forces, limiting the accuracy of its predictions for my experiment.

B OUNDARY LAYER THEORY This theory states that viscous effects for flow over a wing at low

and high

are confined to a thin

layer around the wing’s surface. Outside this layer, viscous forces are insignificant. Fig.3 shows this:

3

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

5

Figure 3 Boundary layer flow over an airfoil To note:

Pressure forces dominate at high

Inviscid (pressure-only) flow analysis is accurate for high

Boundary layer separation occurs at high

. flow.

(Fig.4).

6

Figure 4 Wake formation behind an airfoil beyond the critical angle of attack

Fig.4 is referred to as a stall, which is reached after a near-linear increase in ̃ as in Fig.5:

5

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 14. Print.

6

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 15. Print.

4

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

3 2

4

1

7

1.

Figure 5 Lift curve of NACA 0012 airfoil ̃ increases as a linear function of .

2. Pressure build-up on top of the wing eventually causes partial boundary layer separation, flattening the slope. 3. At “maximum” , a Fig.4 wake occurs. Airfoil geometry influences the sharpness of this “cusp”. 4. Lift rapidly decreases. Beyond

, lift becomes independent of airfoil shape.8

T HIN AIRFOIL THEORY The thickness of an airfoil with maximum thickness

of chord length has little effect on the

pressure forces acting on it. Thin airfoil theory uses this to simplify such an airfoil to a thin filament (Fig.7, Appendix G).

T HIN AIRFOIL THEORY A PPLIED TO TRAILING - EDGE FLAPS Deflection of a plain flap changes the wing camber line, and the resulting changes in aerodynamic characteristics may be calculated from thin airfoil theory assuming zero flow separation.

7

"AeroCFD Operating Instructions." AeroRocket Simulation Software for Rockets and Airplanes. Web. 20 Nov. 2011. . 8

Phillips, Warren F. "1.4 Inviscid Aerodynamics." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print.

5

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

W H AT

AR E P L AI N TR AI L I N G - E D G E F L A P S ?

Some aft portion of an airfoil is hinged to make a plain trailing-edge flap (Fig.6); rotating it about the hinge axis produces a flap-deflection angle

(Fig.7). A downward deflection increases camber, so is

considered positive. 9

Figure 6 An airfoil section with a deflected flap

A P P L YI N G For small

FL AP S T O A ‘ TH I N AI R F OI L ’

and , thin airfoil theory can predict the effects of flap deflection on lift. Development of

below-given equations is in Appendix H. Fig.7 shows the geometric meaning of terms used in subsequent equations:

9

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 39. Print.

6

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 10

Figure 7 Thin airfoil flap approximation Flap chord fraction is: (

)

Ideal section flap effectiveness is:

Lift coefficient for an airfoil with a plain flap is: ̃ (

)

̃

[

( )

]

is section flap effectiveness (accuracy evaluated in Appendix B):

and

are the section flap hinge efficiency and deflection efficiency (Appendix A).

Using above formulae, one deduces ̃ , then ̃ from ̃

̃

, and

from the lift-curve x-

intercept.

H YPOTHESIS

10

Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 40. Print.

7

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

P HYSICS - BASED In a positive plain flap deflection, airfoil camber is increased so air over the top surface has “less space” to travel in than on the bottom surface. From the Law of Continuity:

Hence, decreased cross-sectional area Bernoulli’s Law as dynamic pressure

Lower

will increase airspeed

from

increases:

on top increases lift so a positive correlation with

Lift is a multiple of lift coefficient; ̃ and decrease for positive

and decrease static pressure

should exist.

should also be in positive correlation.

should

as extra lift will have to be suppressed with more negative angles of attack;

there should be a negative correlation between

and .

T HIN - AIRFOIL BASED A spreadsheet (Appendix D) is created using thin airfoil equations to simulate the effect of

on

,

̃ , and ̃ . Results:

8

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Calculated L versus α for various δ 400.0

300.0

200.0

-10° -5°

100.0 L (/gf)

0° 5° 10° 0.0

-20

-15

-10

-5

0

5

10

15

20

25

15° 20° 25°

-100.0

-200.0

-300.0

α (/°)

9

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Calculated CL versus α for various δ 4.0

3.0

2.0 CL (/dimensionless)

-10°

-20

-5° 1.0

0° 5° 10°

0.0 -15

-10

-5

0

5

10

15

20

25

15° 20°

25°

-1.0

-2.0

-3.0

α (/°)

αL0 vs. δ plot 4

2 0

αL0 (/°)

-15

-10

-5

-2

0

5

10

15

20

25

30

-4 -6

Thin airfoil theory

-8 -10 -12 -14 -16

δ (/°)

10

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 Physics-based reasoning was correct- positive

increases lift/lift coefficient and decreases

. This is

an accepted textbook fact, so what I am looking for is the accuracy to which my wind tunnel will match these predictions. NB: thin airfoil theory ignores stall, so I will be able to determine the effect of

on the stall angle of

attack only from wind tunnel tests. Note that lift coefficients greater than 3.0 cannot be achieved on a NACA 2412 airfoil with a plain flap, and high-end coefficients of 2.0 are unlikely to be recorded in my limited wind tunnel. The accuracy of thin airfoil values is hence dubious, but the demonstrated relationship may not be.

E XPERIMENTAL DESIGN & PROCEDURE D ESIGN A 3m home-made wind tunnel with a 0.30mX0.30mX0.30m test section is used. A ProTronik Pro72210 electric motor spinning a 0.254mX0.119m propeller blows air through the tunnel at an average speed of 4.1 ms-1. A NACA 2412 airfoil (Fig.8) is used for the wing; it’s 12% of chord maximum thickness makes it applicable for thin airfoil approximation. The wing is rectangular with 0.300m span and 0.095m chord; the aspect ratio is 3.2. It is made from Styrofoam enclosed in plywood and heat-shrink plastic to reduce friction drag; hinged rods extend through the tunnel floor from its ideal quarter-chord aerodynamic center to a 2 D.P. balance measuring wing mass. A steel rod is hinged to the wing to seamlessly control . An acrylic cover encloses the test section to prevent flow leakage. The wing is mounted at 0.15m above the tunnel floor, almost touching the tunnel sides with the wingtips to reduce effects of finite wingspan.

11

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

11

Figure 8 NACA 2412 airfoil A plain flap is hinged at the trailing edge such that the

ratio is 0.36c below which thin-airfoil

theory produces high error (Appendix B) and above which only marginal

increase is observed12.

Flap deflection is controlled manually. A flow straightener positioned before the test section minimizes the spin the rotating propeller gives to the airflow. Appendix E shows an apparatus diagram.

M ETHOD Independent variable: flap deflection

(/°).

Dependent variables: lift ̃ (/gf13). The method’s aim is to provide a way of collecting lift data accurately (to be converted later to ̃ , , and stall angle

parameters). To collect lift data in /gf:

1. Introduce a 2 D.P. balance underneath the wind tunnel and rest on it an MDF base attached to the wing via rods through the tunnel floor. a. Make sure the balance is zeroed prior to step 1.

11

Photograph. UIUC Airfoil Coordinates Database. Web. 20 Nov. 2011. . 12

Ira H. Abott, Alber E. Von Doenhoff. Theory of Wing Sections. United States: McGraw-Hill Book Company, Inc., 1959. 13

Grams-force (equivalent to grams).

12

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 2. The lift force is to be tested in grams for a range of -10°-25° for

and -15°-20° for , both in

5° increments, so construct an appropriate table/spreadsheet in Excel. 3. Enter an equation “=massbefore-massafter” in the cell for the appropriate

and

condition,

where the massbefore value is the wing mass prior to turning on the fan. 4. First test all positive , so begin by adjusting the wing to 0° alpha and -10° delta. Hence, fill in for massbefore. a. Adjust

by adjusting the wing chord in reference to a protractor mounted in the test

section centered at the wing’s pivot point. b. Adjust

manually with another protractor.

5. Turn on the engine to full throttle and fill in for massafter, completing the equation for the appropriate spreadsheet cell. a. Turn off the engine to save battery. 6. Repeat steps 3-5 for all positive alpha 0°-20° and delta -10°-25°. a. Keep controlled variables constant (Appendix J). 7. Flip the protractor measuring

to repeat steps 3-5 for the negative alpha range, also in 5°

increments. 8. Having taken all raw lift measurements, Excel makes it easy to translate them into

,

,

and ̃ values from graphical analysis and equations in the theoretical section of this paper. 9. Clear up. Process data. Draw a conclusion/evaluation.

S AFETY The fan spins at over 6000 RPM so presents a potential hazard. A fine chicken wire mesh installed at the fan duct prevented accidental contact with the fan’s plane of rotation.

W IND TUNNEL TEST RESU LTS Appendix E presents raw/processed data tables. Notice the absence of error bars due to only one trial of data being collected; collecting more trials to enable error bar calculation is a future improvement. 13

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

̃

VS .

PLOTS

Empirical lift curves for -10°-25° :

L versus α for various δ 60

50

40

30 -10° -5° 20 L (/gf)

0° 5° 10°

10

15° 20° 0 -20

-15

-10

-5

25° 0

5

10

15

20

25

-10

-20

-30

α (/°)

The lift curves follow standard lift curve form. A linear part for small

exists where lift increase is

linear; the curves then level off and the slope becomes negative as the wing stalls at high . This is

14

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 expected from boundary layer theory as the boundary layer separates from the upper surface beyond the stall angle. For 0° , stall occurs at 15°

14.

There was evident friction in my data collection mechanism; as a result, my lift data is lower than the thin airfoil theory predictions, for which the lift slopes are:

Calculated L versus α for various δ 400.0

300.0

200.0 -10° -5° 100.0 L (/gf)

0° 5° 10°

0.0 -20

-15

-10

-5

0

5

10

15

20

25

15° 20° 25°

-100.0

-200.0

-300.0

α (/°)

Note, however, that thin airfoil theory ignores wing stall, in which case theoretical positive lift increments beyond 15°

would be unachievable even in a 100% accurate wind tunnel experiment.

Experimental and theoretical lift slopes show that positive flap deflections translate the =0° lift curve vertically upwards, and downwards for negative flap deflections. Therefore, even though the 14

Evaluation check: the stall angle has a ± few degrees uncertainty as

was taken at 5° intervals.

15

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 magnitude my experimental lift values are below theoretical results, the upward shift of the lift slope is definitely correct as it is backed by both theory and experiment. Judging from data for small , this horizontal translation is almost constant each time15. As proof, one graphs

against

(in degrees):

Lmax vs. δ 70 60

Lmax (/gf)

50 40 Wind tunnel data

30

Linear (Wind tunnel data) 20 10 0 -20

-10

0

10

20

30

δ (/°)

The average linear best-fit shows what the theoretical variation of

could be which, from

inspection of Fig. 9, is most likely the case.

15

Discrepancies at larger alpha may be caused by increasing friction between wing rods and tunnel floor due to higher lift and drag forces

16

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 𝛼 decreases linearly with 𝛿

Notice the very consistent shift upwards of the lift curves with 𝛿.

16

Figure 9 Typical trend for a NACA 66(215)-216 airfoil with 0.20c plain flap My data also shows that the angle of maximum lift coefficient generally decreases with positive flap deflection- this is a trend likewise demonstrated by Fig. 9. Plotting change in ̃

angle,

, versus

:

16

Photograph. Theory of Wing Sections. United States: McGraw-Hill Book, 1959. 195. Print.

17

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

α0 vs. δ plot 18 16 14

12 α0 (/°)

10 Wind tunnel data

8

Linear (Wind tunnel data)

6 4 2 0 -20

-10

0

10

20

30

δ (/°)

Since I was measuring lift data for 5°

increments, I could not capture the gradual decrease in

hence a linear trend line was plotted which shows the likely change in

;

as hypothesized by Fig. 9.

Note from Fig. 10 that the accurate stall angle for the NACA 2412 airfoil is in fact around 14°-16°, which shows that my collected data is roundabout accurate in terms of stall angle at 0° . Hence,

increases the maximum lift of a wing as shown by the positive correlation between

and ̃

. Additionally, there is negative correlation between

and

.

18

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

17

Figure 10 Lift slope for the NACA 2412 airfoil (𝛿=0°)

̃

VS .

PLOTS

A ̃ plot was obtained from its equation in the introduction:

17

Photograph. Theory of Wing Sections. United States: McGraw-Hill Book, 1959. 478. Print.

19

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

CL versus α for various δ 0.7

0.6

0.5

0.4 -10° CL (/dimensionless)

0.3

-5° 0° 5°

0.2

10° 15°

0.1

20° 25°

0.0 -20

-15

-10

-5

0

5

10

15

20

25

-0.1

-0.2

-0.3

α (/°)

The slope of the linear section of graphs above is used to compare lift curves; a steeper linear part suggests that a wing creates more lift per alpha. The discrepancy in lift slopes for =0° between my results and those from NACA (Fig. 10) (their slope: 0.105 deg-1, mine: 0.024 deg-1) may be attributed to friction in my data collection mechanism which would impeded lift increase by friction factor

.

Notice that ̃ is a multiple of ̃ from the section lift equation, so all analysis and evaluation from the previous section applies and will not be repeated here. My experiment has also shown the following relationship between

and the flap deflection

(in

degrees): 20

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

ΔCLmax vs. δ 0.8

ΔCLmax (/dimensionless)

0.7 0.6 0.5 0.4

Wind tunnel data

0.3

Linear (Wind tunnel data)

0.2 0.1 0.0

-20

-10

0

10

20

30

δ (/°)

increases the maximum lift coefficient as shown by the positive correlation between ̃

and

. VS .

PLOTS

My data confirms the hypothesized negative correlation between Comparing wind tunnel data to thin airfoil predictions for Flap deflection (/°)

and

.

and graphing:

αL0 (/°) Empirical

αL0 (/°) Theory

-10

2

3

-5

0

1

0

-2

-2

5

-4

-5-

10

-6

-7

15

-7

-10

20

-19

-12

25

N/A

-15

21

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

αL0 vs. δ plot 5

0 -15

-10

-5

0

5

10

15

20

25

30

αL0 (/°)

-5

Wind tunnel data

-10

Thin airfoil theory

-15

-20

-25

δ (/°)

22

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Linear fit lines calculated with Vernier LoggerPro®

An outlier (ignored for linear fit)

23

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 The theoretical

vs.

slope (=-0.517) appears more negative than the experimental slope (=-0.371).

Notice that thin airfoil theory overestimates equals experimental

for

for negative

and underestimates for positive , and

. This may be due to the theory’s neglect for viscous effects which

perhaps increase with flap deflection due to higher drag. There is a large jump in

between the 15°-20° deflections, and no data for =25°. This is because

my lift curves flatten for negative alpha of large . As higher

increases lift/drag, the rods connecting

the wing to the 2D.P. balance would rub more against their tunnel floor holes, preventing seamless lift force transmission- producing the “leveling off” effect. Thus at large

the extrapolated

value

appears unnaturally low, creating the jump seen above. My results should not be a benchmark for the theory or the theory for my results- my tunnel lacks accuracy due to friction in the data collection mechanism whereas thin airfoil theory wrongfully ignores viscous effects. The values from both are therefore dubious in magnitude, but it is certain that there is a negative correlation between and .

C ONCLUSION ON RELATIO NSHIP BETWEEN

AND

̃ , ̃ , AND

True to my hypothesis, there exists a positive correlation between ̃ correlation between ̃ correlation between

and , a negative correlation between

and , a positive and , and a negative

and . It is of great interest for the engineer and the pilot to know that the

stall angle of attack decreases linearly with positive flap deflection; as a result, it is crucial that the airplane takes off and lands at lower

than usual so as to avoid a stall and a subsequent crash. For a

further investigation in flap deflection effects on aerodynamic properties, I should investigate drag. I predict there would be a proportional rise in the section drag and drag coefficients with increased flap deflection as flow separation and frontal area facing the free stream airflow would increase.

S CRUTINY

24

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

O F METHOD AND APPARATUS The Reynolds number in my experiment was

. This is smaller by 2 orders of magnitude from

the values used in for Fig. 1018. Notice that the lowest comparable19 ̃ 10 was achieved under the lowest

of

value from graph (ο) in Fig.

. The small magnitudes of my ̃ may therefore be

explained by my lower Reynolds number. I may increase my ̃ values by raising

through

increasing airspeed, the chord of the wing, or the fluid viscosity by using something like water (although this is unrealistic for my tunnel). These improvements are questionable in their usefulness as I am merely proving a trend; however, engineers designing planes like the Airbus A380 will need accurate values. The test chamber I used also prevented me from achieving entirely accurate data. From a forum about my tunnel: “Y O U ’ R E … G O I N G T O F I N D T H A T W I T H A 12 X 12 I N C H T E S T A R E A … Y O U ' R E G O I N G TO SUFFER INTERFERENCE FROM THE WAL LS, BOTTOM AND TOP OF THE TEST AREA WITH AIRFOILS IN THE

3 TO 4 INCH CHORD RANGE… IN FULL SIZE WIND

TUNNELS… THE MODELS BEING TES TED ARE TYPICALLY LESS THAN O F T H E C R O S S S E C T I O N O F T H E T E S T A R E A .”

1/10 T H E S I Z E

20

Compression of airflow and wingtip vortices has thus likely offset the accuracy of my results. To improve, I would need to reduce wing size to satisfy above conditions (in which case wingtip vortices would be present), and/or increase the size of the test section (this is not feasible as my tunnel is stationed in school).

18

Fig. 10 is not my own data.

19

The shallowest curve (Δ) is for a rougher, incomparable wing section.

20

BMatthews. RC Universe. s.d. 19 July 2011 .

25

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 One of the largest shortcomings was friction in the data collection mechanism of wing rods against tunnel floor and the wing against the acrylic container in trying to reduce wingtip effects21. The wing rods also had turbulent circular cross-sections; they could be reshaped into symmetric airfoils such as the NACA 0012. The steel rod for changing

was also circular. To avoid this, one could buy

university-grade apparatus, but a more feasible solution may be to implement simple harmonic motion (Appendix I). The accuracy of

and

used, and

was measured in 5° increments, this presented over 20% uncertainty in the

and

measurement could also be improved. As a protractor of 1° uncertainty was

readings! More accurate methods of measuring these variables are implemented in university-grade apparatus in attaching the wing to a device which sets it at an accurate angle while measuring the forces acting on the wing, such as in Fig. 11. 22

Figure 11 A three-component balance designed for use with the AF100 Subsonic Wind Tunnel.

Thin airfoil theory, as previously mentioned, is also worth evaluating. This theory is a tremendous simplification which allows quick performance predictions for aircraft operating at high operated at low

. My wing

so the considerable flow separation and viscous forces acting on it were ignored by

this theory! Hence whereas both empirical and theoretical results agreed on the trend between ̃ and , they rarely agreed on the magnitudes of these values. Thin airfoil theory also ignores stall- an

21

This means reducing wingtip vortices to make the section lift coefficient applicable

22

TecQuipment. s.d. 19 July 2011 .

26

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 important performance factor- so could not predict factors like factors such as separation over my wing at low

. The turbulent flow

also explains the relative irregularity of my data compared to the

linearity of thin airfoil theory that assumes no flow separation.

O F WIND TUNNEL Found through this paper are textbook facts. Presented alone, these give limited value to the extended essay as flap deflection effects on lift are common engineering knowledge. My essay goes beyond information in such books as it evaluates a homemade wind tunnel’s abilities to predict a known aerodynamic relationship. The good. Lift data collected in a homemade wind tunnel enable an engineer to extrapolate results to a wide range of performance features- lift coefficient, maximum lift alpha, effect of zero-lift alpha, etc. These relationships have been compared against recognized sources in this essay and all were correct. An engineer seeking experimental evidence from a wind tunnel will also find these trends; he/she will also have more time than I did and, by collecting data for more alpha and perhaps buying a more powerful engine to increase

, he/she will make patterns in this essay more refined (such as for

)

and thus get better results than I did. The bad. A wind tunnel’s job is to show both trends and values of correct/accurate magnitude. In designing aircraft, it is of little use to an engineer to merely know the trend- he/she must also know the value, such as the maximum lift coefficient. He/she may design a failed aircraft thinking

is 0.7

from an inaccurate homemade wind tunnel test when it is in fact 1.4. As a result, CFD23 methods will be much more useful as they will reveal both patterns and correct values. What makes wind tunnels still useful is their ability to predict what CFD cannot- a wind tunnel must hence be more accurate than a computer code. In the case of my homemade wind tunnel, even though it reveals the trends, its construction is painstaking and will not pay off as its accuracy will be inferior

23

CFD: Computational Fluid Dynamics.

27

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 to that of computer simulation. In my case, CFD will ultimately be both faster and more accurate than a wind tunnel- and this is a topic for a whole another extended essay. Nevertheless, the data achieved in my tunnel enabled me to draw conclusions consistent with those achieved in much more expensive, professional-grade aerodynamic testing facilities. To what extent can a homemade wind tunnel predict the effect of

on wing performance? To the extent of trends, not

of correct values; as a result, what I found is that my wind tunnel enabled me to find the trends I was looking for, and they were correct trends. Never mind that I did not get accurate actual magnitudes of ̃ or ̃ - my wind tunnel enabled me to construct an experimentally-supported argument, and that was its aim. As for an engineer, he/she should seek more elaborate testing facilities and CFD methods to fulfill his/her needs. Word Count: 3’999/4’000

28

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

B IBLIOGRAPHY Internet: "Aerodynamics Definition." NASA. NASA. Web. 14 July 2011. . BMatthews. RC Universe. s.d. 19 July 2011 . Books: Phillips, Warren F. "1.1 Introduction and Notation." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print. Phillips, Warren F. "1.4 Inviscid Aerodynamics." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print. Phillips, Warren F. "1.6 Incompressible Flow over Airfoils." Mechanics of Flight. Hoboken, NJ: Wiley, 2004. Print. Ira H. Abott, Alber E. Von Doenhoff. Theory of Wing Sections. United States: McGraw-Hill Book Company, Inc., 1959. Video/audio/photo: TecQuipment. s.d. 19 July 2011 . Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 27. Print. Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 261. Print. Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 14. Print. Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 15. Print.

29

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 "AeroCFD Operating Instructions." AeroRocket Simulation Software for Rockets and Airplanes. Web. 20 Nov. 2011. . Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 39. Print. Photograph. Mechanics of Flight. Hoboken, NJ: Wiley, 2010. 40. Print. Photograph. Theory of Wing Sections. United States: McGraw-Hill Book, 1959. 195. Print. Photograph. Theory of Wing Sections. United States: McGraw-Hill Book, 1959. 478. Print. Database photos : Photograph. UIUC Airfoil Coordinates Database. Web. 20 Nov. 2011. .

30

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

A PPENDICES A Section flap hinge efficiency, section flap effectiveness,

, and deflection efficiency,

, are used in the equation for calculating

:

The values for these parameters are deduced from the following graphs:

Figure A.1 Section flap hinge efficiency for sealed trailing-edge flaps. For unsealed flaps (as in my case) these values should be reduced by 20%.

31

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

Figure A.2 Section flap deflection efficiency for sealed trailing-edge flaps. For deflections less than 10°, a deflection efficiency of 1.0 should be used.

32

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

B As seen in Fig. B.1, the section flap effectiveness predicted by thin airfoil theory correlates well to the more complex vortex panel method which takes thickness into account (this method is beyond the scope of this text), but overestimates the actually flap effectiveness calculated from experiment (Fig. B.1 is not my own data).

Figure B.1 Section flap effectiveness compared amongst thin airfoil theory, vortex panel method, and experimental data. As we can see, thin airfoil theory always overestimates actual section flap effectiveness. This is because, in reality, the hinge mechanism about the flap causes local boundary layer separation and flow leakage from the high-pressure bottom surface to the lower-pressure top surface, and this causes the section flap effectiveness to reduce as it is a factor of the section flap hinge efficiency

as in

. In addition, at deflections greater than 10°, error associated with the ideal section flap

33

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029 effectiveness for

becomes significant, resulting in the implementation of the factor

in the equation

whose value is calculated from Appendix A.

From Fig. B.1 we see that for a flap chord fraction like mine of about 0.36, the discrepancy in theoretical and experimental results is only about 7%, whereas for smaller flap chord fractions of about 0.1 the error rises to almost 25%. As a result, a flap chord fraction like mine is a good choice for the application of thin airfoil theory as it reaches a good compromise which allows for a small enough error yet provides large enough maximum section lift coefficient increments to reduce percentage error in data as per Abbott and Doenhoff24 and yet does not dominate too much of the airfoil geometry by the flap.

24

Ira H. Abott, Alber E. Von Doenhoff. Theory of Wing Sections. United States: McGraw-Hill Book Company, Inc., 1959.

34

Danylo Malyuta; International School of Geneva: Campus des Nations; Candidate Number: 002169-029

C As was mentioned in the main body of the text, thin airfoil theory is a method belonging to a field of inviscid aerodynamics that ignores viscous effects on the forces acting on airborne bodies. Thin airfoil theory is in good agreement with experimental data for low speeds and small

for airfoils

of thickness

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