chapter 3 analysis of naca 4 series...

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CHAPTER 3

ANALYSIS OF NACA 4 SERIES AIRFOILS

The baseline characteristics and analysis of NACA 4 series airfoils

are presented in this chapter in detail. The correlations for coefficient of lift

and drag have been developed and compared with the existing results.

The effects of Reynolds number on coefficient of lift and drag for various

airfoils are predicted and presented. The basics of NACA airfoils, the

developed correlations and the effect of Reynolds number are discussed in the

next subsequent sections.

3.1 NACA AIRFOILS

The selection of blade profiles for wind rotors was based on NACA

(National Advisory Committee for Aeronautics). The standard practices of

lettering and numbering adopted by NACA for profiles of airfoils are

followed. In general, airfoils are specified by maximum camber height in terms

of percentage of the chord in terms of percentage of chord. For example,

NACA 4412, the first number used on profiles refers to height (gradient

height) on y-axis as percentage ratio based on the fact that the profile is

situated at the center of a coordinate system. Whereas, the second digit refers

to its location on x-axis as percentage ratio and last two digits indicate the

thickness of blade profile as percentage ratio (Dreese 2000). In the above

example, the first digit ‘4’ indicates the maximum height of the camber is

expressed as a percentage of the airfoil length (i.e.) 4 percentage, the next

digit ‘4’ represents the horizontal location of the maximum camber in terms

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of a chord length (40%), the last two digits ‘12’ expresses the maximum

thickness of the airfoil expressed as a percentage of the airfoil chord length.

The airfoil with camber, camber line, leading edge, trailing edge and chord

length are shown in Figure 3.1.

Figure 3.1 Airfoil geometry

The aim of this study is to present the aerodynamic characteristics

of the blade sections which are the most crucial parameter of a wind turbine

blade. Some of the NACA profiles are selected for analysis and Reynolds

number, Angle of attack, Chord length, Sliding rate, Coefficient of lift and

drag have been taken into concern.

3.2 CORRELATIONS FOR COEFFICIENT OF LIFT AND DRAG

The coefficient of lift (Cl) and co efficient of drag (Cd) for any

airfoil is based on the following parameters.

Geometry of the airfoil like maximum camber height,

maximum camber position and thickness.

Angle of attack (AOA)

Wind velocity ( )

56

Research studies have been conducted to evaluate different airfoils

and found out the coefficient of lift and drag for various airfoils and published

their findings. Jacobs et al. (1935) conducted wide range of experiments by

varying the airfoil geometrical parameters and angle of attack and wind

velocity for various NACA airfoils and published the results of coefficient of

lift and drag for 68 airfoils. They conducted experiments in a variable density

wind tunnel by keeping a constant velocity of 68.4 ft/s. They have plotted the

graph for various angles of attack with the values of ratio for a large

group of related airfoils. They have confined their experimental work with the

angle of attack ranging from -8o to 10o and due consideration has been given

for the viscous effects and the phenomenon of stall at higher angle of attack.

They have varied the horizontal camber position from 0% to 60% in steps of

20%, vertical camber position from 0% to 7% with a step of 1%, the thickness

0% to 21% in steps of 3%.

The predictions for coefficient of lift and drag for the airfoils with

parameters other than the above are difficult and need an experimental set-up.

Hence, it involves higher cost and time and for study of numerical and

simulation with various parameters, the above practical results finds limited

applications. Hence there is a need for developing the correlations capable of

giving the coefficient of lift and drag for any NACA 4 series by specifying the

angle of attack and wind velocity.

The correlations are developed with above objective using the

experimental results published by Jacobs et al. (1935) and checked for various

NACA profiles and further modified suitably for giving better results for any

airfoils. The coefficient of lift and drag for various NACA profiles have been

taken from the published work of Jacobs et al. (1935) for various angle of

attack and velocity by interpolation and extrapolation. The sample of results

thus obtained for the NACA 4410 is given in Table A1.1 in Appendix 1.

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The correlation for coefficient of lift and drag depends upon the airfoil

geometry, angle of attack and wind velocity. The linest function method ()

(y=m1x1+m2x2+m3x3+b) is used to develop the correlation.

The correlation to find coefficient of lift and drag can be written as

shown below.

= [( × 4 ) + ( × ) + ( × ) + ] (3.1)

Where

4XXX - Airfoil geometry in usual notation

AOA - Angle of attack in degrees

- Wind velocity in m/s

C1, C2, C3 & C4 - Constants to be evaluated

Using a best fit straight line regression method, the constant C1, C2,

C3 & C4 are obtained for coefficient of lift and drag separately using the

function available in M.S. Excel software as ‘Linest’, substituted in the

equation (3.1) and presented below in equations (3.2) and (3.3).

C = {( 0.01374 × 4XXX) + (0.046252 × AOA) + (0.000433 × ) +

61.26981} (3.2)

C = {( 0.00012571 × 4XXX) + (0.001441 × AOA) + ( 0.00037 × ) +

0.573138} (3.3)

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The statistical measures for the correlation (3.2) is given below

R2 (Coefficient of determination) is 0.755

Standard error for C1 is 0.000539, C2 is 0.000508, C3 is 0.000601

C4 is 2.65and Cl is 0.2037

The statistical measures for the correlation (3.3) is given below

R2 (Coefficient of determination) is 0.823

Standard error for C1 is 1.36e-5, C2 is 1.29e-5, C3 is 1.52e-5

C4 is 0.067and Cd is 0.0051

In order to improve the R2 value, the correlations are modified by

refining the constants C1, C2, C3 & C4 for coefficient of lift and drag

separately. The correlations are applied to various airfoils that are grouped as

shown below.

I Group - NACA4401 to NACA4410

II Group - NACA4411 to NACA4420

III Group - NACA4421 to NACA4430

IV Group - NACA4431 to NACA4440

The procedure followed in the modifications of constants

(C1, C2, C3 & C4) for predicting coefficient of lift and drag are separately

discussed in the following subsections 3.2.1 and 3.2.2.

3.2.1 Modified Correlation for Coefficient of Lift

The correlation used to evaluate the coefficient of lift in equation

(3.2) is considered and modified to yield results closer to the experimental

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results by identifying the terms C1 and C2 as these two parameters are directly

related to the geometry of the airfoil. The other two terms C3 & C4 are

assumed to be constant. The term C3 is associated with wind velocity and not

directly related to the geometry of the profile. Further, the term C4 is an

independent constant. In the equation (3.2) the values of C3 and C4 and are

taken as 0.000433 and 61.26981 respectively in the modified correlation.

However any profile may be considered for evaluating the constants, NACA

4415 is chosen to evaluate the modified values of C1 and C2. The modified

values are substituted in equation (3.2) for the coefficient of lift of NACA

4415 with an angle of attack as 0o and -8o.

By substituting 0º angle of attack in the equation (3.2) the term C2

becomes zero and the term C1 can be arrived by equating the coefficient of lift as 0.3 which is the experimental result derived from Jacobs et al. (1935) for the wind velocity 21.1831 m/s.

{( × 4415) + ( × 0) + (0.000433 × 21.1831) + 61.26981} = 0.3

0.013811

The modified value of C2 is evaluated by substituting the angle of attack as -8o and experimental coefficient of lift as -0.3, the modified value of C1 in the equation (3.2) as shown below.

{( 0.013811 × 4415) + [ × ( 8)] + (0.000433 × 21.1831)+ 61.26981} = 0.3

= 0.080575

By substituting the modified constants and in equation (3.2), the revised correlation for coefficient of lift is obtained as in equation (3.4).

= {( 0.013811 × 4 ) + (0.080575 × ) + (0.000433 × ) + 61.26981} (3.4)

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The revised correlation (3.4) is applied to NACA 4412 airfoil

which belongs to the Group II as mentioned above and the coefficient of lift is

verified. The variation of the coefficient of lift with respect to angle of attack

for NACA 4412 is shown in Figure 3.2.

-0.5

0.0

0.5

1.0

1.5

-10 -5 0 5 10 15

Angle of attack (Degree)

NACA 4412Wind velocity 21.18 m/s

Cl (wind tunnel)

Cl (Correlation)

Figure 3.2 Validation of coefficient of lift of NACA 4412

It is evident from the Table 3.1 and Figure 3.2 that the revised

correlation with modified constants yields much closer results. The

correlation can be applied to any profile coming under the Group II (NACA

4411 to NACA 4420).

The above procedure was adopted for other Groups and the revised correlation with modified constants. In Group I, the values corresponding to NACA 4406 is used to obtain the modified constants and the revised correlation is shown in the equation (3.5). The modified constants are given below.

C1 = -0.01384, C2 = 0.075075

The above constants are substituted in equation (3.2) with the values corresponding to NACA 4409 series airfoil and the results are compared with the experimental values and presented Figure 3.3.

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-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-10 -5 0 5 10 15



Cl (wind tunnel)

Cl (Correlation)


= {( 0.01384 × 4 ) + (0.075075 × ) + (0.000433 × ) +

61.26981} (3.5)

The above correlation is suitable of predicting coefficient of lift for

any profile in Group I (NACA 4401- NACA 4410).

From the equations (3.5) and (3.4) corresponding to Group I and II,

the modified constants C1 and C2 are given in Table 3.1.

Table 3.1 Modified constants C1 and C2

Group C1 C2

Group I -0.01384 0.075075

Group II -0.013811 0.080575

The difference between the constants C1 of Group I and II is

2.9 x 10-5 . Similarly, the difference between the constant C2 of Group I and

Group II is 0.55 x 10-2. The constants corresponding to Group III can be

obtained by adding the difference with the value of constant corresponding to

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Group II and the corresponding revised correlation for Group III is given in

equation (3.6).

0.013811 + 2.9 10 = 0.01378

= 0.080575 + 0.55 10 = 0.86075

= {( .013788 × 4 ) + (0.86075 × ) + (0.000433 × ) + 61.26981} (3.6)

The above constants are used in finding the coefficient of lift for

the airfoil NACA 4421 (Group III) and it is compared with the experimental

data for validation and the results are given in Figure 3.4. In the same way,

the constants corresponding to Group IV can also be evaluated.

-0.5

0.0

0.5

1.0

1.5

-10 -5 0 5 10 15



Cl (wind tunnel)

Cl (Correlation)


Thus the general correlation with modified constants of C1 and C2

can be written as shown in the equation (3.7).

= {( × (2.3 × 10 ) + ( 0.01384 × 4 ) +

( × (0.55 × 10 )) + (0.075075 × ) +

(0.000433 × ) + 61.26981} (3.7)

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Values of ‘M’ in equation (3.7) for various Groups of airfoils are

shown in Table 3.2.

Table 3.2 Values of ‘M’ for NACA airfoils

M 0 1 2 3

NACA Airfoil 4401-4410 4411-4420 4421-4430 4431-4440

By substituting the values of ‘M’ in equation (3.7) the value of

for various airfoils is obtained. The R2 value for the correlation (3.7) is

identified as 0.92. Hence, the above correlation proved the goodness of the fit

with experimental results.

The correlation developed is also useful in predicting power

coefficient of wind turbine systems and in reducing the time and cost. For the

airfoil shapes not having experimental results, the above correlation will be

useful in determining the coefficient of lift and other useful parameters.

3.2.2 Modified Correlation for Coefficient of Drag

Similar to the correlation for coefficient of lift, the correlation for

finding coefficient of drag is also developed and modified further to yield

closer results to the experimental values. In this section, the step by step

procedure adopted for developing correlation for finding coefficient of drag is

illustrated.

Let us consider the basic correlation in equation (3.3). The terms C1

and C2 are modified as detailed in the section 3.2.1 by keeping other two

terms C3 & C4 constant and their values are -0.00037 and 0.573138

respectively. As discussed in the previous section, in the modification of

correlation for finding coefficient of drag, NACA 4415 is considered. The

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modified terms C1 and C2 are calculated by substituting the AOA and wind

velocity. The AOA varied from -8o to 100 and the wind velocity is fixed as

21.1831 m/s. While substituting AOA as 0º in the equation (3.3) the term C2

becomes zero and the term C1 can be arrived by equating the coefficient of

drag as 0.018 which is the experimental result for the above wind velocity.

(( × 4415) + ( × 0) + ( 0.00037 × 21.1831 ) + (0.573138) = 0.018

1 0.000123986

The modified term 2 is evaluated by substituting the value of term

1 in the equation (3.3). As the AOA varied from -8o to 100 in the

experimental result, 2 is separately calculated for negative angle of attack

(-8o to 0o) and positive angle of attack (0o to 100). The value of 2 is

determined by selecting angle of attack as -5o with the corresponding

experimental coefficient of drag.

(( 0.000123986 × 4415) + × ( 5) + ( 0.00037 × 20.9095) +(0.573138) = 0.01775

0.00025015

The value of above is substituted in equation (3.3) and the

correlation for coefficient of drag for negative angle of attack (( ( )) is

derived and is shown in equation (3.8). The term C2 is the same for all

selected group of airfoils as the coefficient of drag ( ) remains the same for

negative values of angle of attack (-8º to 0º).

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( ) = {( 0.000123986 × 4 ) + ( 0.00025015 × )

+ ( 0.00037 × ) + 0.573138}

In a similar way, the modified value of term C2 is determined for

the positive angle of attack (0º to 10º) by considering angle of attack as 6º

with corresponding experimental coefficient of drag ( ) as 0.0373.

( 0.000123986 × 4415) + ( × 6) + ( 0.00037 × 20.9095) + (0.573138)= 0.0373

= 0.00446

By substituting the term C1 and C2, the correlation of coefficient of

drag for the positive angle of attack ( ( ))is developed and shown in

equation (3.9).

( ) = {( 0.000123986 × 4 ) + (0.00446 × ) +

( 0.00037 × ) + 0.573138 }

The revised correlations (3.8) and (3.9) are applied to NACA

4412 airfoil of Group II, the coefficient of drag is found out. The graph

showing the variation of the coefficient of drag with respect to angle of attack

is shown in Figure 3.5.

(3.9)

(3.8)

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0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

-10 -5 0 5 10 15



Cd (Wind tunnel)

Cd (Correlation)

Figure 3.5 Validation of coefficient of drag of NACA 4412

As it is seen in the case of coefficient of lift, the revised correlation

for coefficient of drag also yields closer values with experimental values for

various AOA that is illustrated using the Figure 3.5. The above correlation

can be applied to any profile of Group II (NACA 4411 to NACA 4420).

In order to validate the consistency of the correlation for different

airfoils of other groups, the above correlation is applied for the airfoil of

group I with the same procedure. The NACA 4406 is used to obtain

the modified constants and revised correlation and it is shown in the

equation (3.10).

The term C1 and the terms C2 for both negative and positive angle

of attack is also found out and given below. The term C1 is same for both

negative and positive angle of attack for an airfoil group.

0.000124155 0.00025015

0.000124155 = 0.00433

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The modified terms C1 and C2 are substituted in equation (3.3) and

revised correlation for Coefficient of drag for negative and positive angle of

attack are shown in equation (3.10) and (3.11) respectively.

) = {( 0.000124155 × 4 ) + ( 0.00025015 × ) +( 0.00037 × ) + 0.573138} (3.10)

(+ ) = {( 0.000124155 × 4 ) + (0.00433 × ) +( 0.00037 × ) + 0.573138} (3.11)

The above equations (3.10) and (3.11) are applied to NACA 4409

airfoil and analyzed. The results are illustrated graphically in Figure 3.6.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

-10 -5 0 5 10 15



Cd (Wind tunnel)

Cd (Correlation)


The above revised correlations (3.10) and (3.11) are suitable for

predicting coefficient of drag of any profile in Group I. The values of terms

C1 and C2 for Group I and II are given in the Table 3.3.

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Table 3.3 Values of C1 and C2 of Group I & II

Group C1 for AOA (-8o to 10o)

C2 for AOA (-8o to 0o)

C2 for AOA (0o to 10o)

Group I -0.000124155 -0.00025015 0.00433

Group II -0.000123986 -0.00025015 0.00446

As described in the previous section, the difference between the

constants is added to predict the constants of other preceding groups. The

difference between the term C1 of Group I and II is 1.69 x 10-7. Similarly, the

difference between the term C2 for negative angle of attack of Group I and II

is zero. Further, the difference between the constant C2 for positive angle of

attack of Group I and II is 1.3 x 10-4. The terms C1 and C2 corresponding to

Group III is obtained by adding the difference between the terms which

belongs to Group I and II with the term corresponding to Group II as shown

below.

= 0.000123986 + 1.69 × 10 0.000123817 (AOA -8o to 10o)

0.00025015 + 0 = 0.00025015 (AOA -8o to 0o)

= 0.0446 + 1.3 × 10 = 0.00459 (AOA 0o to 10o)

The revised correlation for negative and positive angle of attack is

given in equations (3.12) and (3.13) respectively.

( ) = {( 0.000123817 × 4 ) + ( 0.00025015 × ) +

( 0.00037 × ) + 0.573138} (3.12)

( ) = {( 0.000123817 × 4 ) + (0.00459 × ) +

( 0.00037 × ) + 0.573138} (3.13)

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The above constants are used in finding the coefficient of drag for the airfoil NACA 4421 (Group III) and it is compared with the experimental values for validation. The values are graphical illustrated in Figure 3.7.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

-10 -5 0 5 10 15



Cd (Wind tunnel)

Cd (Correlation)


In the same way, the constants corresponding to Group IV are also

be evaluated. The generalized correlation for predicting the coefficient of drag

for any profile belonging to any group is formulated and given in the

equations (3.14) and (3.15). The value of ‘M’ is given in the Table 3.7 for

various Groups.

( ) = {( × (1.69 × 10 ) + ( 0.000124155 × 4 ) +

( 0.0002501 × ) + ( 0.00037 × ) + 0.573138} (3.14)

( ) = {( × (1.69 × 10 ) + ( 0.000124155 × 4 ) +

( × (1.3 × 10 )) + (0.00433 × ) +

( 0.00037 × ) + 0.573138} (3.15)

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The R2 value for the correlation (3.14) is found as 0.93 and for

correlation (3.15) is 0.91. Hence the above correlations are confirmed with the

experimental results.

The above correlations developed for coefficient of lift and drag are

being used to analyze the effect of Reynolds number on lift and drag forces of

airfoils and discussed elaborately in the forthcoming subsections of this

chapter. The same correlations have also been used in optimization of power

coefficient using genetic algorithm and it is presented in chapter 5.

3.3 EFFECT OF REYNOLDS NUMBER ON LIFT AND DRAG

In this section, the effect of Reynolds number (Re) on coefficient of

lift (Cl) and drag (Cd) has been analyzed. This study is useful in determining

the characteristics of blade profile and cross section that will be used in

optimizing the design and thereby reduces the manufacturing cost. Further,

the ratio of lift and drag (sliding rate) which is a function of ‘C l’ and ‘Cd’ has

been evaluated with respect to Re. The Re is varied from 100000 to 200000 in

steps of 25000. The various airfoils of NACA series are considered for

analysis. The modified correlations developed in the previous section are used

to evaluate ‘Cl’ and ‘Cd’.

In general, the rotor diameter varies from 2 to 100m and chord

length varies from 0.1 to 5m depending on the power generation. Piggott

(2000) predicted that Re varied with respect to chord length (c), wind velocity

(v) and the geometry of the airfoil. He suggested the following equation

(3.16) relating the above parameters.

= 68500 (3.16)

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Where, the constant 68500 is proposed by him to represent the ratio

of air density and viscosity. The chord length is a significant factor for blade

profile. It is the length between the leading edge and the trailing edge.

Further, he proposed the following equation (3.17) to predict the chord length

(c) using rotor diameter (D), tip speed ratio ( ) and number of blades (N).

= (3.17)

In the above equation the tip speed ratio ( ) is calculated using the

following equation (3.18).

= (3.18)

The velocity triangle as discussed by Lee and Flay (1999) for an

airfoil is shown in Figure 3.8 that indicates the lift and drag forces, AOA ( ),

pitch angle ( ), air inflow angle ( ) wind velocity (v), velocity of rotor ( r)

and relative velocity (W).

Figure 3.8 Blade velocity diagram

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From the tip speed ratio, the rotor linear velocity ( r) can be

calculated and using the above velocity triangle, wind inflow angle ( ) can

be determined using the following equation (3.19).

tan = v / r (3.19)

The angle of attack ( ) can be found out as and are known.

The lift and drag forces are calculated by the following equations

(3.20) and (3.21).

( ) = (3.20)

( ) = (3.21)

Where - Density of air, kg/m3

c - Chord length, m

r - Radius of the blade element, m

W - Relative velocity of air in m/s = v + ( r)

The Sliding rate ( ) is defined as the ratio between the Lift (L)

and Drag (D). In the above equation (3.20) and (3.21) as other parameters for

a particular airfoil are the same, the sliding rate can also be taken as ratio

between coefficient of lift and drag and is given as the equation (3.22).

= Cl/Cd (3.22)

In this work, the NACA series airfoils of NACA 4410, NACA

4412, NACA 4414, NACA 4416, NACA 4418 and NACA 4420 are

considered for analysis. For the airfoil NACA 4410, the sliding rate has been

evaluated for the angle of attack from 0o to 10o at Re=100000 and it is

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presented in the Table 3.4. The coefficient of lift and drag has also been

evaluated using modified correlations and used in predicting sliding rate.

Table 3.4 Sliding rate for various AOA

NACA 4410, Re 100000

S.NO AOA (Degree) Cl Cd L/D

1 0 0.573 0.0100 57.30

2 1 0.699 0.0105 66.57

3 2 0.802 0.0106 75.66

4 3 0.878 0.0111 79.10

5 4 0.946 0.0116 81.55

6 5 1.007 0.0120 83.92

7 6 1.060 0.0131 80.92

8 7 1.106 0.0143 77.34

9 8 1.145 0.0156 73.40

10 9 1.178 0.0171 68.89

11 10 1.204 0.0189 63.70

The above values have been shown in Figure 3.9 as a graph to show

the variation of sliding rate with respect to AOA. From the Figure 3.9 it is

noticed that at 5o of AOA, the sliding rate attains the maximum value of 83.92

and hence the power output is optimum at the conditions specified above.

74

Figure 3.9 Variation of L/D ratio for various angle of attack

The same procedure is adopted for predicting optimum sliding rate

for various airfoils by varying angle of attack from 0o to 10o, Reynolds

number in the range of 100000 to 200000 in steps of 25000. The results are

shown as graph in Figures 3.10(a) to 3.10(e)

Figure 3.10(a) Variation of sliding rate for various angle of attack at

Re =100000

75

For Reynolds number 100000, the optimum angle of attack at the

highest sliding rate for various NACA airfoils are depicted in Figure 3.10(a)

as 5o that yielded optimum power output.

30

35

40

45

50

55

60

65

70

75

0 1 2 3 4 5 6 7 8 9 10

Angle of Attack (Degree)

NACA 4410

NACA 4412

NACA 4414

NACA 4416

NACA 4418

NACA 4420

Figure 3.10(b) Variation of sliding rate for various angle of attack at

Re =125000

The optimum sliding rate for NACA 4410 and NACA 4412 is

arrived at 4o of angle of attack, where as for other airfoils it is at 5o of angle of

attack for the Reynolds number 125000.

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30

35

40

45

50

55

60

65

70

75

80

0 1 2 3 4 5 6 7 8 9 10


NACA 4410NACA 4412NACA 4414NACA 4416NACA 4418NACA 4420

Figure 3.10(c) Variation of sliding rate for various angle of attack at

Re =150000

Various NACA airfoils yield the optimum sliding rate at 5o of angle

of attack for Reynolds number 150000.

35

40

45

50

55

60

65

70

75

80

0 1 2 3 4 5 6 7 8 9 10


NACA 4410

NACA 4412

NACA 4414

NACA 4416

NACA 4418

NACA 4420

Figure 3.10(d) Variation of sliding rate for various angle of attack at

Re =175000

The airfoils NACA 4410, NACA 4412, NACA 4414, and

NACA 4416 have optimum sliding rate at 5o of angle of attack whereas

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NACA 4418 and NACA 4420 have optimum sliding rate at 6o of angle of

attack for Reynolds number 175000.

40

45

50

55

60

65

70

75

80

85

0 1 2 3 4 5 6 7 8 9 10


NACA 4410NACA 4412NACA 4414NACA 4416NACA 4418NACA 4420

Figure 3.10(e) Variation of sliding rate for various angle of attack at

Re =200000

The optimum sliding rate for NACA 4420 is at 6o angle of attack,

other profiles achieved optimum sliding rate at 5o of angle of attack for

Reynolds number 200000. The optimum angle of attack for various NACA

airfoils with respect to Reynolds number is presented in Table 3.5.

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Table 3.5 Optimum angle of attack with respect to Reynolds number

Reynoldsnumber

Optimum Angle of attack (Degree) NACA4410

NACA4412

NACA4414

NACA4416

NACA4418

NACA4420

100000 5 5 5 5 5 5125000 4 4 5 5 5 5150000 5 5 5 5 5 5175000 5 5 5 5 6 6200000 5 5 5 5 5 6

From the above table, it is inferred that the optimum angle of attack

varies from 4o to 6o for different airfoils corresponding to optimum sliding

rate for various Reynolds numbers.

The variation of coefficient of lift (Cl) at various angles of attack

for different airfoils are found out at Reynolds number of 100000 and

presented in Table 3.6. The flow around the airfoil is attached to certain limit

of angle of attack and beyond which the flow is separated from the surface of

the airfoil. Hence, the coefficient of lift increases for all airfoils as the angle

of attack increases and then started decreasing after attaining the maximum

value. This optimum coefficient of lift is attained at 14o to 15o for various

airfoils. The results are shown graphically to show the variation of coefficient

of lift with respect to angle of attack in Figure 3.11.

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Table 3.6 Variation of coefficient of lift with respect to angle of attack

Angle of attack

(Degree)

Coefficient of lift (Cl) at Re =100000

NACA4410

NACA4412

NACA4414

NACA4416

NACA4418

NACA4420

-5 -0.071 -0.069 -0.067 -0.065 -0.063 -0.061

-4 0.047 0.050 0.054 0.058 0.062 0.066

-3 0.165 0.170 0.175 0.181 0.187 0.193

-2 0.282 0.290 0.297 0.304 0.312 0.319

-1 0.400 0.409 0.418 0.428 0.437 0.446

0 0.518 0.529 0.540 0.551 0.562 0.573

1 0.635 0.648 0.661 0.674 0.686 0.699

2 0.753 0.767 0.782 0.796 0.799 0.798

3 0.870 0.886 0.891 0.893 0.880 0.873

4 0.987 0.985 0.979 0.975 0.952 0.940

5 1.100 1.074 1.058 1.048 1.016 0.999

6 1.202 1.154 1.129 1.113 1.073 1.051

7 1.293 1.225 1.191 1.170 1.122 1.096

8 1.372 1.287 1.246 1.220 1.164 1.134

9 1.441 1.341 1.293 1.262 1.200 1.166

10 1.498 1.386 1.331 1.296 1.229 1.192

11 1.545 1.422 1.363 1.324 1.252 1.212

12 1.581 1.450 1.386 1.345 1.269 1.226

13 1.606 1.470 1.403 1.358 1.279 1.234

14 1.619 1.481 1.412 1.365 1.284 1.237

15 1.621 1.484 1.413 1.365 1.283 1.235

16 1.611 1.477 1.407 1.358 1.276 1.228

80

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-10 -5 0 5 10 15 20


NACA 4412

NACA 4414

NACA 4416

NACA 4418

NACA 4420

NACA 4410

Figure 3.11 Variation of coefficient of lift with angle of attack

The airfoil with lower thickness (NACA 4410) have maximum

coefficient of lift than others at higher angle of attack. The coefficient of lift

for various airfoils is very close to each other for angle of attack from -5o to 5o

and started deviating to a larger extent as the angle of attack increases. It

attains the maximum value for the airfoils of NACA 4410, NACA 4412, and

NACA 4414 at 15o and for airfoils of NACA 4416, NACA 4418 and NACA

4420 is at 14o of angle of attack.

3.4 SUMMARY

The baseline characteristics and analysis of NACA 4 series airfoils

are presented in this chapter. The correlations for coefficient of lift and drag

of NACA 4 series airfoils have been developed and compared with the

experimental results. The effects of Reynolds number on coefficient of lift

and drag for various NACA airfoils are predicted using the correlations and

81

presented. The NACA airfoils have higher Lift/Drag ratio at the angle of

attack from 4o to 6o for Reynolds number in the range of 100000 to 200000.

The variation of coefficient of lift (Cl) at various angles of attack for different

airfoils is found out at Reynolds number of 100000. It is found that the airfoil

with lower thickness (NACA 4410) have maximum coefficient of lift than

others at higher angle of attack. The coefficient of lift for various airfoils is

very close to each other for smaller angle of attack and the variations are more

as the angle of attack increases.

chapter 3 analysis of naca 4 series...

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