Aerodynamics Lab 3

Direct Measurement of Airfoil Lift and Drag

David Clark

Group 1

MAE 449 – Aerospace Laboratory

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Abstract

The characterization of lift an airfoil can generate is an important process in the field of

aerodynamics. The following exercise studies a NACA 0012 airfoil with a chord of 4 inches. By varying

the angle of attack at a known Reynolds number, the lift coefficient, Cl, can be determined by using a

two-component dynamometer. Normalizing the lift and drag forces against the reference area, as well

as correcting for some disturbances due to the experiment setup. The lift and drag coefficient calculated

using this setup is less accurate than previous methods.

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Contents

Abstract .................................................................................................................................................. 2

Introduction and Background ................................................................................................................. 4

Introduction ........................................................................................................................................ 4

Governing Equations .......................................................................................................................... 4

Similarity ............................................................................................................................................. 5

Boundary Corrections ......................................................................................................................... 5

Equipment and Procedure ..................................................................................................................... 7

Equipment .......................................................................................................................................... 7

Experiment Setup ............................................................................................................................... 7

Basic Procedure .................................................................................................................................. 8

Data, Calculations, and Analysis ............................................................................................................. 8

Raw Data ............................................................................................................................................ 8

Preliminary Calculations ..................................................................................................................... 9

Results .................................................................................................................................................. 13

Discussion and Conclusions .................................................................................................................. 16

References ............................................................................................................................................ 17

Raw Data .............................................................................................................................................. 17

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Introduction and Background

Introduction

The following laboratory procedure explores the aerodynamic lift and drag forces experienced by a

NACA 0012 cylinder placed in a uniform free-stream velocity. This will be accomplished using a wind

tunnel and various pressure probes along an airfoil as the subject of study.

When viscous shear stresses act along a body, as they would during all fluid flow, the resultant force

can be expressed as a lift and drag component. The lift component is normal to the airflow, whereas the

drag component is parallel.

To further characterize and communicate these effects, non-dimensional coefficients are utilized.

For example, a simple non-dimensional coefficient can be expressed as

�� = ��1

2 ��� � �� �

Equation 1

where F is either the lift or drag forces, AREF is a specified reference area, ρ is the density of the fluid, and

V is the net velocity experienced by the object.

Governing Equations

To assist in determining the properties of the working fluid, air, several proven governing

equations can be used, including the ideal gas law, Sutherland’s viscosity correlation, and Bernoulli’s

equation. These relationships are valid for steady, incompressible, irrotational flow at nominal

temperatures with negligible body forces.

The ideal gas law can be used to relate the following

� = ���

Equation 2

where p is the pressure of the fluid, R is the universal gas constant (287 J/(kg K)), and T is the

temperature of the gas. This expression establishes the relationship between the three properties of air

that are of interest for use in this experiment.

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Another parameter needed is the viscosity of the working fluid. Sutherland’s viscosity

correlation is readily available for the testing conditions and can be expressed as

� = ���.�

1 + ��

Equation 3

where b is equal to 1.458 x 10-6

(kg)/(m s K^(0.5)) and S is 110.4 K.

Finally, Bernoulli’s equation defines the total stagnation pressure as

�� = � + 12 �

Equation 4

Similarity

Using the previous governing equations, we can use the Reynolds number. The Reynolds

number is important because it allows the results obtained in this laboratory procedure to be scaled to

larger scenarios. The Reynolds number can be expressed as

�� = ���

Equation 5

where c is a characteristic dimension of the body. For a cylinder, this dimension will be the diameter. As

a result, the Reynolds number based on diameter is referenced as ReD.

Boundary Corrections

The following experiment must consider three different corrections due to the setup of the

tunnel section.

First, the “squeezing” of the inviscid flow causes the streamlines to flatten and push toward the

center of the test section. This effect is referred to as horizontal buoyancy. To correct for this effect, the

following expressions can be defined.

∆�� = − 6ℎ

" Λ$ %�%&

Equation 6

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$ = "

48 ��ℎ�

Equation 7

The parameters used in these expressions include

• h, the height of the wind tunnel section

• Λ, the body shape factor (estimated from empirical charts)

• dp/dx, the static pressure gradient

• c, the chord of the foil

The second consideration corrects for blockage due to equipment within the wind tunnel itself.

Like the previous correction, simple expressions have been derived to adjust the parameters.

)*+, = Λ$

Equation 8

)*+* = 0.96/01*23425�246678

9

Equation 9

)*+ = )*+, + )*+*

Equation 10

),+ = �/ℎ4 �;4

Equation 11

Though some parameters have already been defined, the corrections for blockage introduce the

following parameters.

• Volstrut, the volume of the strut

• Atunnel, the cross-sectional area of the tunnel

• Cdu, the uncorrected drag coefficient

Finally, the last set of expressions corrects for the presence of the floor and ceiling within the

wind tunnel.

Δ=*> = 57.3$2" B�84 + 3�C>

D4E

Equation 12

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Δ�8,*> = −$�84

Equation 13

Δ�C>D,*> = − 1

4 Δ�8,*>

Equation 14

where

• Clu, the uncorrected lift coefficient

• Cmc/4u, the uncorrected c/4 moment coefficient

The use of each correction equation is further explained in the calculation section.

Equipment and Procedure

Equipment

The following experiment used the following equipment:

• A wind tunnel with a 1-ft x 1-ft test section

• NACA 0012 airfoil section

• A transversing mechanism to move the pitot tube to various sections of the test section

• A Pitot-static probe

• Digital pressure transducer

• Data Acquisition (DAQ) Hardware

• Two-component dynamometer (to measure lift and drag forces)

Experiment Setup

Before beginning, the pressure and temperature of laboratory testing conditions was measured and

recorded. Using equations 2 and 3, the density and viscosity of the air was calculated.

The UAH wind tunnel contains cutouts to allow the NACA airfoil to be mounted inside the test

section. The two-component dynamometer can measure the force exerted perpendicular and parallel to

the airflow, which represent the lift and drag respectively.

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Basic Procedure

To ensure the working flow is relatively laminar and within a range acceptable for study, the

procedure initiated flow with a Reynolds number of 250,000. The velocity at which the laboratory air

must be accelerated was determined by solving equation 5 for velocity. First, the density and viscosity of

the air must be calculated using equations 2 and 3 respectively.

Using the DAQ hardware, the lift and drag at each angle of attack and specified dynamic pressure

was recorded.

Data, Calculations, and Analysis

Raw Data

The following table catalogs the pressure read by the DAQ hardware for the specified rotations.

Three data sets were taken to ensure integrity.

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Data Set 1 Angle Dynamic Pressure Lift Drag

-4 868 -2.50 -0.51

-2 868 -0.65 -0.43

-0.25 867 1.32 -0.28

2 865 2.41 -0.35

4 866 5.77 -0.42

6 867 8.58 -0.54

8 864 9.92 -0.63

10 868 10.90 -0.75

12 867 8.10 -2.95

Data Set 2 Angle Dynamic Pressure Lift Drag

-4 869 1.35 -0.40

-2 868 1.50 -0.38

0 868 3.48 -0.41

2 867 5.83 -0.44

4 868 7.18 -0.50

6 868 8.49 -0.57

8 869 9.23 -0.58

10 867 10.97 -0.77

12 868 8.17 -2.99

Data Set 3 Angle Dynamic Pressure Lift Drag

-4 867 1.35 -0.38

-2 868 1.43 -0.40

0 866 3.03 -0.40

2 867 4.25 -0.42

4 867 5.95 -0.45

6 868 8.43 -0.56

8 867 10.05 -0.67

10 867 10.75 -0.75

12 868 9.30 -2.35

Table 1

Preliminary Calculations

First, the density and viscosity of the air at laboratory conditions was calculated. This can easily be

accomplished using equation 2 and 3.

� = ��� = 99.1GHI

287 JGKL 296.15L

= 1.1660 GKM9

Equation 15

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� = ���.�

1 + ��

=B1.827 × 10OP GK

M R L�.�E S/296.15 L5�.�T1 + 110.4 L

296.15 L= 1.83 × 10� GK

M R

Equation 16

For a Reynolds number of 250,000, the velocity of the airflow must therefore be

= �� �� � =

/2500005 B1.83 × 10� GKM RE

B1.1660 GKM9E /0.1016 × 10O M5

= 38.57 MR

Equation 17

This value is determined using the definition of the Reynolds number where c, the reference length, is

the known value of the chord, 0.1016 meters. For reference, the value for q can be calculated as

UV = 12 � = 1

2 B1.1660 GKM9E �38.57 M

R �

= 867.37 HI

Equation 18

All three data sets can be combined by averaging the three records for each angle.

Averaged Data Angle Lift Drag

-4 0.0667 -0.4300

-2 0.7600 -0.4033

-0.25 1.3200 -0.2800

0 3.2550 -0.4050

2 4.1633 -0.4033

4 6.3000 -0.4567

6 8.5000 -0.5567

8 9.7333 -0.6267

10 10.8733 -0.7567

12 8.5233 -2.7633

Table 2

The lift and drag can be used in equation one to determine the lift and drag coefficients. For

example, for -4 degrees angle of attack

�� = ��1

2 ��� � �� �= 0.0667W

B12 B1.660 GK

M9E �38.57 MR �E /0.03064M5

= 0.0025

Equation 19

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�; = ��1

2 ��� � �� �= 0.4300W

B12 B1.660 GK

M9E �38.57 MR �E /0.03064M5

= 0.0162

Equation 20

Below is a table of the lift and drag coefficients. These lift coefficients must be corrected for the

three corrections mentioned previously.

Averaged Data Angle Lift Coefficient Drag Coefficient

-4 0.0025 0.0162

-2 0.0286 0.0152

-0.25 0.0497 0.0105

0 0.1225 0.0152

2 0.1567 0.0152

4 0.2371 0.0172

6 0.3198 0.0209

8 0.3662 0.0236

10 0.4091 0.0285

12 0.3207 0.1040

Table 3

To begin correcting for horizontal buoyancy, the following parameters need to be calculated.

$ = "

48 ��ℎ�

= "

48 B0.1016M0.3048ME

= 0.0228

Equation 21

∆�� = − 6ℎ

" Λ$ %�%& = − 6/0.3048M5

" /0.35/0.02285 B−120.3 HIM E = 0.1463W

Equation 22

It is important to note Λ is assuming a thickness to chord ratio is 0.3.

)*+, = Λ$ = /0.35/0.02285 = 6.853 × 10O9

Equation 23

)*+* = 0.96/01*23425�9/ = 0.96/5.96 × 10O�M95

/0.0929M59/ = 2.021 × 10O9

Equation 24

The volume of the strut and cross-sectional area were known.

)*+ = )*+, + )*+* = 6.853 × 10O9 + 2.021 × 10O9 = 8.887 × 10O9

Equation 25

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The correction parameters εwb, Δαsc, ΔClsc, and ΔCmc/4sc are calculated on the fly for each angle since

these expressions utilize the uncorrected lift and drag coefficient, which varies for each angle of attack.

For example, for 0 degrees angle of attack

),+ = �/ℎ4 �;4 = 0.1016M/0.3048M

4 /−0.01525 = −0.0013

Equation 26

Δ�8,*> = −/$5/�845 = −/0.02285/0.12255 = −0.0028

Equation 27

Δ�C,>D,*> = − 14 Δ�8,*> = − 1

4 /−0.00285 = 0.0007

Equation 28

To further demonstrate the usage of the correction factors above, the parameters for the zero

angle of attack will all be calculated.

= 4/1 + )*+ + ),+5 = 38.56 MR X1 + /8.874 × 10O95 + /−0.0013 × 10O95Y = 38.86 M

R

Equation 29

U = U4/1 + 2)*+ + 2),+5 = 867.37HIX1 + 2/8.874 × 10O95 + 2/−0.0013 × 10O95Y = 880.87HI

Equation 30

�� = ��4/1 + )*+ + ),+5 = 249947X1 + /8.874 × 10O95 + /−0.0013 × 10O95Y = 251847

Equation 31

= = =4 + 57.3$2" B�84 + 4�C,>D,4E = 0 + 57.3/0.02285

2" X0.1225 + 4/0.00075Y = 0.03 ZI%

Equation 32

�;4 = /�4 − Δ��5U4� = X/0.4050W5 − /0.1463W5Y

/867HI5/0.0306M5 = 0.0208

Equation 33

�; = �;4/1 − 3)*+ − 2),+5 = 0.0208X1 − 3/8.874 × 10O95 − 2/−0.0013 × 10O95Y = 0.0095

Equation 34

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Results

Using the same procedure outlined above, the following table catalogs all the parameters used in

calculating the corrected lift and drag coefficient.

Correction Calculation Summary

Uncorrected Data

Experimental Angle of Attack

Average Dynamic Pressure Reynolds Number Velocity

Lift Coefficient

Drag Coefficient

-4 868.0 250091 38.59 0.0025 0.0162

-2 868.0 250091 38.59 0.0286 0.0152

-0.25 867.0 249947 38.56 0.0497 0.0105

0 867.0 249947 38.56 0.1225 0.0152

2 866.3 249850 38.55 0.1567 0.0152

4 867.0 249947 38.56 0.2371 0.0172

6 867.7 250043 38.58 0.3198 0.0209

8 866.7 249898 38.56 0.3662 0.0236

10 867.3 249995 38.57 0.4091 0.0285

12 867.7 250043 38.58 0.3207 0.1040

Corrected Data / Correction Factors

Experimental Angle of Attack ε,wb

Corrected Dynamic Pressure

Corrected Reynolds Number

Corrected Velocity ΔCl,sc

-4 0.0013 885.75 252647 38.98 -0.0001

-2 0.0013 885.60 252626 38.98 -0.0007

-0.25 0.0009 883.91 252384 38.94 -0.0011

0 0.0013 884.59 252482 38.96 -0.0028

2 0.0013 883.90 252384 38.94 -0.0036

4 0.0014 884.87 252523 38.96 -0.0054

6 0.0017 886.10 252698 38.99 -0.0073

8 0.0020 885.46 252607 38.97 -0.0084

10 0.0024 886.84 252806 39.01 -0.0093

12 0.0087 898.10 254428 39.26 -0.0073

Corrected Data / Correction Factors

Experimental Angle of Attack

Corrected Angle of Attack ΔCm,c/4,sc Cl Cdu Cd

-4 -4.00 0.0000 0.0024 0.0107 0.0104

-2 -1.99 0.0002 0.0274 0.0097 0.0094

-0.25 -0.24 0.0003 0.0476 0.0050 0.0049

0 0.03 0.0007 0.1172 0.0097 0.0095

2 2.03 0.0009 0.1499 0.0097 0.0094

4 4.05 0.0014 0.2268 0.0117 0.0113

6 6.07 0.0018 0.3057 0.0154 0.0150

8 8.08 0.0021 0.3499 0.0181 0.0175

10 10.09 0.0023 0.3906 0.0230 0.0222

12 12.07 0.0018 0.3021 0.0984 0.0941

Table 4

Figure 1 contains the various lift coefficients versus angle of attack for all the methods described

previously, as well as the previous lab session.

-0.5000

0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

-4.00 -2.00 0.00

Cl

Figure 1

contains the various lift coefficients versus angle of attack for all the methods described

previously, as well as the previous lab session.

2.00 4.00 6.00 8.00

Angle of Attack (Degrees)

Cl versus Angle of Attack

Force Measurement Method (Lab 3)

Pressure Method (Lab 2)

Xfoil Results

NACA Data (Re=130000)

Naca Data (Re=330000)

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contains the various lift coefficients versus angle of attack for all the methods described

10.00 12.00

0.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

0.0350

0.0400

-4.00 -2.00 0.00

Cd

Figure 2

0.00 2.00 4.00 6.00

Angle of Attack

Cd versus Angle of Attack

Force Measurement Method (Lab 3)

Xcode Results

NACA 0012 (Re=170000)

NACA 0012 (Re=330000)

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8.00 10.00

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Figure 3

Discussion and Conclusions

Comparing the lift coefficient curves plotted in figure 1, the pressure measurement method

most closely matches the NACA data. The worst method was the force measurement technique, which

was the only method that did not recognize zero lift at a zero angle of attack. The Reynolds number had

very little effect on the lift coefficient.

The best method for determining the drag coefficient is the force measurement method. As

Reynolds number increases, the amount of drag decreases.

The accuracy of the computer simulation is dubious. The software would not solve reliably, and

several data points were off the charts.

The force measurement method should not be the recommended procedure for determining

the lift and drag coefficients due to the poor control and lack of repeatability.

-40

-20

0

20

40

60

80

100

-4 -2 0 2 4 6 8 10 12

L/D

Angle of Attack

L/D versus Angle of Attack

Force Measurement Method (Lab 3)

Xfoil Results

NACA 0012 (Re=170000)

NACA 0012 (Re=330000)

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References

“Aerodynamics Lab 3 – Direct Measurement of Airfoil Lift and Drag.” Handout

Raw Data

Aero Lab 1

Fall 07

R= 287

p 99100 b= 0.000001458

t 23 S= 110.4 T= 296.15

row 1.165950252 c= 0.1016

u 1.82773E-05 Re= 250000

q 867.3710308 span= 0.3016

V 38.57246947 Aref 0.030643

Data Set 1

Angle experimental

angle experimental

q Lift Drag

-4 -4 868 -0.25 -0.051

-2 -2 868 -0.065 -0.043

0 -0.25 867 0.132 -0.028

2 2 865 0.241 -0.035

4 4 866 0.577 -0.042

6 6 867 0.858 -0.054

8 8 864 0.992 -0.063

10 10 868 1.09 -0.075

12 12 867 0.81 -0.295

Data Set 2

Angle experimental

angle experimental

q Lift Drag

-4 -4 869 0.135 -0.04

-2 -2 868 0.15 -0.038

0 0 868 0.348 -0.041

2 2 867 0.583 -0.044

4 4 868 0.718 -0.05

6 6 868 0.849 -0.057

8 8 869 0.923 -0.058

10 10 867 1.097 -0.077

12 12 868 0.817 -0.299

Data Set 3

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Angle experimental

angle experimental

q Lift Drag

-4 -4 867 0.135 -0.038

-2 -2 868 0.143 -0.04

0 0 866 0.303 -0.04

2 2 867 0.425 -0.042

4 4 867 0.595 -0.045

6 6 868 0.843 -0.056

8 8 867 1.005 -0.067

10 10 867 1.075 -0.075

12 12 868 0.93 -0.235