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NACA airfoil

The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA). The shape of the NACA airfoils is described using a series of digits following the word "NACA". The parameters in the numerical code can be entered into equations to precisely generate the cross-section of the airfoil and calculate its properties.

Profile geometry – 1: Zero-lift line; 2: Leading edge; 3: Nose circle; 4: Max. thickness; 5: Camber; 6: Upper surface; 7: Trailing edge; 8: Camber mean-line; 9: Lower surface
Profile lines – 1: Chord, 2: Camber, 3: Length, 4: Midline
A: blue line = chord, green line = camber mean-line, B: leading-edge radius, C: xy coordinates for the profile geometry (chord = x axis; y axis line on that leading edge)

Origins

NACA initially developed the numbered airfoil system which was further refined by the United States Air Force at Langley Research Center. According to the NASA website:

During the late 1920s and into the 1930s, the NACA developed a series of thoroughly tested airfoils and devised a numerical designation for each airfoil — a four digit number that represented the airfoil section's critical geometric properties. By 1929, Langley had developed this system to the point where the numbering system was complemented by an airfoil cross-section, and the complete catalog of 78 airfoils appeared in the NACA's annual report for 1933. Engineers could quickly see the peculiarities of each airfoil shape, and the numerical designator ("NACA 2415," for instance) specified camber lines, maximum thickness, and special nose features. These figures and shapes transmitted the sort of information to engineers that allowed them to select specific airfoils for desired performance characteristics of specific aircraft.[1]

Four-digit series

The NACA four-digit wing sections define the profile by:[2]

  1. First digit describing maximum camber as percentage of the chord.
  2. Second digit describing the distance of maximum camber from the airfoil leading edge in tenths of the chord.
  3. Last two digits describing maximum thickness of the airfoil as percent of the chord.[3]

For example, the NACA 2412 airfoil has a maximum camber of 2% located 40% (0.4 chords) from the leading edge with a maximum thickness of 12% of the chord.

The NACA 0015 airfoil is symmetrical, the 00 indicating that it has no camber. The 15 indicates that the airfoil has a 15% thickness to chord length ratio: it is 15% as thick as it is long.

Equation for a symmetrical 4-digit NACA airfoil

 
Plot of a NACA 0015 foil generated from formula

The formula for the shape of a NACA 00xx foil, with "xx" being replaced by the percentage of thickness to chord, is[4]

 [5][6]

where:

x is the position along the chord from 0 to 1.00 (0 to 100%),
  is the half thickness at a given value of x (centerline to surface),
t is the maximum thickness as a fraction of the chord (so t gives the last two digits in the NACA 4-digit denomination divided by 100).

Note that in this equation, at x = 1 (the trailing edge of the airfoil), the thickness is not quite zero. If a zero-thickness trailing edge is required, for example for computational work, one of the coefficients should be modified such that they sum to zero. Modifying the last coefficient (i.e. to −0.1036) will result in the smallest change to the overall shape of the airfoil. The leading edge approximates a cylinder with a chord-normalized radius of

 [7]

Now the coordinates   of the upper airfoil surface and   of the lower airfoil surface are

 

Symmetrical 4-digit series airfoils by default have maximum thickness at 30% of the chord from the leading edge.

Equation for a cambered 4-digit NACA airfoil

 
Plot of a NACA 2412 foil. The camber line is shown in red, and the thickness – or the symmetrical airfoil 0012 – is shown in purple.

The simplest asymmetric foils are the NACA 4-digit series foils, which use the same formula as that used to generate the 00xx symmetric foils, but with the line of mean camber bent. The formula used to calculate the mean camber line is[4]

 

where

m is the maximum camber (100 m is the first of the four digits),
p is the location of maximum camber (10 p is the second digit in the NACA xxxx description).

For example, a NACA 2412 airfoil uses a 2% camber (first digit) 40% (second digit) along the chord of a 0012 symmetrical airfoil having a thickness 12% (digits 3 and 4) of the chord.

For this cambered airfoil, because the thickness needs to be applied perpendicular to the camber line, the coordinates   and  , of respectively the upper and lower airfoil surface, become[8]

 

where

 
 

Five-digit series

The NACA five-digit series describes more complex airfoil shapes.[9] Its format is LPSTT, where:

  • L: a single digit representing the theoretical optimal lift coefficient at ideal angle of attack CLI = 0.15 L (this is not the same as the lift coefficient CL),
  • P: a single digit for the x coordinate of the point of maximum camber (max. camber at x = 0.05 P),
  • S: a single digit indicating whether the camber is simple (S = 0) or reflex (S = 1),
  • TT: the maximum thickness in percent of chord, as in a four-digit NACA airfoil code.

For example, the NACA 23112 profile describes an airfoil with design lift coefficient of 0.3 (0.15 × 2), the point of maximum camber located at 15% chord (5 × 3), reflex camber (1), and maximum thickness of 12% of chord length (12).

The camber line for the simple case (S = 0) is defined in two sections:[10]

 

where the chordwise location   and the ordinate   have been normalized by the chord. The constant   is chosen so that the maximum camber occurs at  ; for example, for the 230 camber line,   and  . Finally, constant   is determined to give the desired lift coefficient. For a 230 camber-line profile (the first 3 numbers in the 5-digit series),   is used.

Non-reflexed 3 digit camber lines

3-digit camber lines provide a very far forward location for the maximum camber.

The camber line is defined as[10]

 

with the camber line gradient

 

The following table presents the various camber-line profile coefficients:

Camber-line profile      
210 0.05 0.0580 361.40
220 0.10 0.126 51.640
230 0.15 0.2025 15.957
240 0.20 0.290 6.643
250 0.25 0.391 3.230

Reflexed 3-digit camber lines

Camber lines such as 231 makes the negative trailing edge camber of the 230 series profile to be positively cambered. This results in a theoretical pitching moment of 0.

From  

 

From  

 

The following table presents the various camber-line profile coefficients:

Camber-line profile        
221 0.10 0.130 51.990 0.000764
231 0.15 0.217 15.793 0.00677
241 0.20 0.318 6.520 0.0303
251 0.25 0.441 3.191 0.1355

Modifications

Four- and five-digit series airfoils can be modified with a two-digit code preceded by a hyphen in the following sequence:

  1. One digit describing the roundness of the leading edge, with 0 being sharp, 6 being the same as the original airfoil, and larger values indicating a more rounded leading edge.
  2. One digit describing the distance of maximum thickness from the leading edge in tenths of the chord.

For example, the NACA 1234-05 is a NACA 1234 airfoil with a sharp leading edge and maximum thickness 50% of the chord (0.5 chords) from the leading edge.

In addition, for a more precise description of the airfoil all numbers can be presented as decimals.

1-series

A new approach to airfoil design pioneered in the 1930s, in which the airfoil shape was mathematically derived from the desired lift characteristics. Prior to this, airfoil shapes were first created and then had their characteristics measured in a wind tunnel. The 1-series airfoils are described by five digits in the following sequence:

  1. The number "1" indicating the series.
  2. One digit describing the distance of the minimum-pressure area in tenths of chord.
  3. A hyphen.
  4. One digit describing the lift coefficient in tenths.
  5. Two digits describing the maximum thickness in percent of chord.

For example, the NACA 16-123 airfoil has minimum pressure 60% of the chord back with a lift coefficient of 0.1 and maximum thickness of 23% of the chord.

6-series

An improvement over 1-series airfoils with emphasis on maximizing laminar flow. The airfoil is described using six digits in the following sequence:

  1. The number "6" indicating the series.
  2. One digit describing the distance of the minimum pressure area in tenths of the chord.
  3. The subscript digit gives the range of lift coefficient in tenths above and below the design lift coefficient in which favorable pressure gradients exist on both surfaces.
  4. A hyphen.
  5. One digit describing the design lift coefficient in tenths.
  6. Two digits describing the maximum thickness as percent of chord.
  7. "a=" followed by a decimal number describing the fraction of chord over which laminar flow is maintained. a=1 is the default if no value is given.


For example, the NACA 612-315 a=0.5 has the area of minimum pressure 10% of the chord back, maintains low drag 0.2 above and below the lift coefficient of 0.3, has a maximum thickness of 15% of the chord, and maintains laminar flow over 50% of the chord.

7-series

Further advancement in maximizing laminar flow achieved by separately identifying the low-pressure zones on upper and lower surfaces of the airfoil. The airfoil is described by seven digits in the following sequence:

  1. The number "7" indicating the series.
  2. One digit describing the distance of the minimum pressure area on the upper surface in tenths of the chord.
  3. One digit describing the distance of the minimum pressure area on the lower surface in tenths of the chord.
  4. One letter referring to a standard profile from the earlier NACA series.
  5. One digit describing the lift coefficient in tenths.
  6. Two digits describing the maximum thickness as percent of chord.

For example, the NACA 712A315 has the area of minimum pressure 10% of the chord back on the upper surface and 20% of the chord back on the lower surface, uses the standard "A" profile, has a lift coefficient of 0.3, and has a maximum thickness of 15% of the chord.

8-series

Supercritical airfoils designed to independently maximize laminar flow above and below the wing. The numbering is identical to the 7-series airfoils except that the sequence begins with an "8" to identify the series.

See also

References

  1. ^ Allen, Bob (31 January 2017). "NACA Airfoils". nasa.gov. NASA. Retrieved 27 July 2020.
  2. ^ E. N. Jacobs, K. E. Ward, & R. M. Pinkerton. NACA Report No. 460, "The characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel". NACA, 1933.
  3. ^ "Fundamentals of aerodynamics", John D. Anderson, Jr., third ed., ch. 4.
  4. ^ a b Moran, Jack (2003). An introduction to theoretical and computational aerodynamics. Dover. p. 7. ISBN 0-486-42879-6.
  5. ^ Aerospaceweb.org | Ask Us - NACA Airfoil Series
  6. ^ Payne, Greg (8 Jul 1994), , archived from the original on April 27, 2009
  7. ^ Gordon J. Leishman. Principles of Helicopter Aerodynamics. p. 361.
  8. ^ Marzocca, Pier. "The NACA airfoil series" (PDF). Clarkson University. Retrieved July 5, 2016.
  9. ^ E. N. Jacobs & R. M. Pinkerton 1936 Test in the variable-density wind tunnel of related airfoils having the maximum camber unusually far forward, NACA Report No. 537.
  10. ^ a b Abbott, Ira; von Doenhoff, Albert (1959). Theory of Wing Sections: Including a Summary of Airfoil Data. New York: Dover Publications. p. 115. ISBN 978-0486605869.

External links

naca, airfoil, airfoil, shapes, aircraft, wings, developed, national, advisory, committee, aeronautics, naca, shape, described, using, series, digits, following, word, naca, parameters, numerical, code, entered, into, equations, precisely, generate, cross, sec. The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics NACA The shape of the NACA airfoils is described using a series of digits following the word NACA The parameters in the numerical code can be entered into equations to precisely generate the cross section of the airfoil and calculate its properties Profile geometry 1 Zero lift line 2 Leading edge 3 Nose circle 4 Max thickness 5 Camber 6 Upper surface 7 Trailing edge 8 Camber mean line 9 Lower surface Profile lines 1 Chord 2 Camber 3 Length 4 Midline A blue line chord green line camber mean line B leading edge radius C xy coordinates for the profile geometry chord x axis y axis line on that leading edge Contents 1 Origins 2 Four digit series 2 1 Equation for a symmetrical 4 digit NACA airfoil 2 2 Equation for a cambered 4 digit NACA airfoil 3 Five digit series 3 1 Non reflexed 3 digit camber lines 3 2 Reflexed 3 digit camber lines 4 Modifications 5 1 series 6 6 series 7 7 series 8 8 series 9 See also 10 References 11 External linksOrigins EditNACA initially developed the numbered airfoil system which was further refined by the United States Air Force at Langley Research Center According to the NASA website During the late 1920s and into the 1930s the NACA developed a series of thoroughly tested airfoils and devised a numerical designation for each airfoil a four digit number that represented the airfoil section s critical geometric properties By 1929 Langley had developed this system to the point where the numbering system was complemented by an airfoil cross section and the complete catalog of 78 airfoils appeared in the NACA s annual report for 1933 Engineers could quickly see the peculiarities of each airfoil shape and the numerical designator NACA 2415 for instance specified camber lines maximum thickness and special nose features These figures and shapes transmitted the sort of information to engineers that allowed them to select specific airfoils for desired performance characteristics of specific aircraft 1 Four digit series EditThe NACA four digit wing sections define the profile by 2 First digit describing maximum camber as percentage of the chord Second digit describing the distance of maximum camber from the airfoil leading edge in tenths of the chord Last two digits describing maximum thickness of the airfoil as percent of the chord 3 For example the NACA 2412 airfoil has a maximum camber of 2 located 40 0 4 chords from the leading edge with a maximum thickness of 12 of the chord The NACA 0015 airfoil is symmetrical the 00 indicating that it has no camber The 15 indicates that the airfoil has a 15 thickness to chord length ratio it is 15 as thick as it is long Equation for a symmetrical 4 digit NACA airfoil Edit Plot of a NACA 0015 foil generated from formula The formula for the shape of a NACA 00xx foil with xx being replaced by the percentage of thickness to chord is 4 y t 5 t 0 2969 x 0 1260 x 0 3516 x 2 0 2843 x 3 0 1015 x 4 displaystyle y t 5t left 0 2969 sqrt x 0 1260x 0 3516x 2 0 2843x 3 0 1015x 4 right 5 6 where x is the position along the chord from 0 to 1 00 0 to 100 y t displaystyle y t is the half thickness at a given value of x centerline to surface t is the maximum thickness as a fraction of the chord so t gives the last two digits in the NACA 4 digit denomination divided by 100 Note that in this equation at x 1 the trailing edge of the airfoil the thickness is not quite zero If a zero thickness trailing edge is required for example for computational work one of the coefficients should be modified such that they sum to zero Modifying the last coefficient i e to 0 1036 will result in the smallest change to the overall shape of the airfoil The leading edge approximates a cylinder with a chord normalized radius of r 1 1019 t 2 displaystyle r 1 1019t 2 7 Now the coordinates x U y U displaystyle x U y U of the upper airfoil surface and x L y L displaystyle x L y L of the lower airfoil surface are x U x L x y U y t y L y t displaystyle x U x L x quad y U y t quad y L y t Symmetrical 4 digit series airfoils by default have maximum thickness at 30 of the chord from the leading edge Equation for a cambered 4 digit NACA airfoil Edit Plot of a NACA 2412 foil The camber line is shown in red and the thickness or the symmetrical airfoil 0012 is shown in purple The simplest asymmetric foils are the NACA 4 digit series foils which use the same formula as that used to generate the 00xx symmetric foils but with the line of mean camber bent The formula used to calculate the mean camber line is 4 y c m p 2 2 p x x 2 0 x p m 1 p 2 1 2 p 2 p x x 2 p x 1 displaystyle y c begin cases dfrac m p 2 left 2px x 2 right amp 0 leq x leq p dfrac m 1 p 2 left 1 2p 2px x 2 right amp p leq x leq 1 end cases where m is the maximum camber 100 m is the first of the four digits p is the location of maximum camber 10 p is the second digit in the NACA xxxx description For example a NACA 2412 airfoil uses a 2 camber first digit 40 second digit along the chord of a 0012 symmetrical airfoil having a thickness 12 digits 3 and 4 of the chord For this cambered airfoil because the thickness needs to be applied perpendicular to the camber line the coordinates x U y U displaystyle x U y U and x L y L displaystyle x L y L of respectively the upper and lower airfoil surface become 8 x U x y t sin 8 y U y c y t cos 8 x L x y t sin 8 y L y c y t cos 8 displaystyle begin aligned x U amp x y t sin theta amp y U amp y c y t cos theta x L amp x y t sin theta amp y L amp y c y t cos theta end aligned where 8 arctan d y c d x displaystyle theta arctan frac dy c dx d y c d x 2 m p 2 p x 0 x p 2 m 1 p 2 p x p x 1 displaystyle frac dy c dx begin cases dfrac 2m p 2 left p x right amp 0 leq x leq p dfrac 2m 1 p 2 left p x right amp p leq x leq 1 end cases Five digit series EditThe NACA five digit series describes more complex airfoil shapes 9 Its format is LPSTT where L a single digit representing the theoretical optimal lift coefficient at ideal angle of attack CLI 0 15 L this is not the same as the lift coefficient CL P a single digit for the x coordinate of the point of maximum camber max camber at x 0 05 P S a single digit indicating whether the camber is simple S 0 or reflex S 1 TT the maximum thickness in percent of chord as in a four digit NACA airfoil code For example the NACA 23112 profile describes an airfoil with design lift coefficient of 0 3 0 15 2 the point of maximum camber located at 15 chord 5 3 reflex camber 1 and maximum thickness of 12 of chord length 12 The camber line for the simple case S 0 is defined in two sections 10 y c k 1 6 x 3 3 r x 2 r 2 3 r x 0 lt x lt r k 1 r 3 6 1 x r lt x lt 1 displaystyle y c begin cases dfrac k 1 6 big x 3 3rx 2 r 2 3 r x big amp 0 lt x lt r dfrac k 1 r 3 6 1 x amp r lt x lt 1 end cases where the chordwise location x displaystyle x and the ordinate y displaystyle y have been normalized by the chord The constant r displaystyle r is chosen so that the maximum camber occurs at x p displaystyle x p for example for the 230 camber line p 0 3 2 0 15 displaystyle p 0 3 2 0 15 and r 0 2025 displaystyle r 0 2025 Finally constant k 1 displaystyle k 1 is determined to give the desired lift coefficient For a 230 camber line profile the first 3 numbers in the 5 digit series k 1 15 957 displaystyle k 1 15 957 is used Non reflexed 3 digit camber lines Edit 3 digit camber lines provide a very far forward location for the maximum camber The camber line is defined as 10 y c k 1 6 x 3 3 r x 2 r 2 3 r x 0 lt x lt r k 1 r 3 6 1 x r lt x lt 1 displaystyle y c begin cases dfrac k 1 6 big x 3 3rx 2 r 2 3 r x big amp 0 lt x lt r dfrac k 1 r 3 6 1 x amp r lt x lt 1 end cases with the camber line gradient d y c d x k 1 6 3 x 2 6 r x r 2 3 r 0 lt x lt r k 1 r 3 6 r lt x lt 1 displaystyle frac dy c dx begin cases dfrac k 1 6 big 3x 2 6rx r 2 3 r big amp 0 lt x lt r dfrac k 1 r 3 6 amp r lt x lt 1 end cases The following table presents the various camber line profile coefficients Camber line profile p displaystyle p r displaystyle r k 1 displaystyle k 1 210 0 05 0 0580 361 40220 0 10 0 126 51 640230 0 15 0 2025 15 957240 0 20 0 290 6 643250 0 25 0 391 3 230Reflexed 3 digit camber lines Edit Camber lines such as 231 makes the negative trailing edge camber of the 230 series profile to be positively cambered This results in a theoretical pitching moment of 0 From x c r displaystyle frac x c leq r y c k 1 6 x c r 3 k 2 k 1 1 r 3 x c r 3 x c r 3 displaystyle frac y c frac k 1 6 left left frac x c r right 3 frac k 2 k 1 1 r 3 frac x c r 3 frac x c r 3 right From r lt x c 1 0 displaystyle r lt frac x c leq 1 0 y c k 1 6 k 2 k 1 x c r 3 k 2 k 1 1 r 3 x c r 3 x c r 3 displaystyle frac y c frac k 1 6 left frac k 2 k 1 left frac x c r right 3 frac k 2 k 1 1 r 3 frac x c r 3 frac x c r 3 right The following table presents the various camber line profile coefficients Camber line profile p displaystyle p r displaystyle r k 1 displaystyle k 1 k 2 k 1 displaystyle k 2 k 1 221 0 10 0 130 51 990 0 000764231 0 15 0 217 15 793 0 00677241 0 20 0 318 6 520 0 0303251 0 25 0 441 3 191 0 1355Modifications EditFour and five digit series airfoils can be modified with a two digit code preceded by a hyphen in the following sequence One digit describing the roundness of the leading edge with 0 being sharp 6 being the same as the original airfoil and larger values indicating a more rounded leading edge One digit describing the distance of maximum thickness from the leading edge in tenths of the chord For example the NACA 1234 05 is a NACA 1234 airfoil with a sharp leading edge and maximum thickness 50 of the chord 0 5 chords from the leading edge In addition for a more precise description of the airfoil all numbers can be presented as decimals 1 series EditA new approach to airfoil design pioneered in the 1930s in which the airfoil shape was mathematically derived from the desired lift characteristics Prior to this airfoil shapes were first created and then had their characteristics measured in a wind tunnel The 1 series airfoils are described by five digits in the following sequence The number 1 indicating the series One digit describing the distance of the minimum pressure area in tenths of chord A hyphen One digit describing the lift coefficient in tenths Two digits describing the maximum thickness in percent of chord For example the NACA 16 123 airfoil has minimum pressure 60 of the chord back with a lift coefficient of 0 1 and maximum thickness of 23 of the chord 6 series EditAn improvement over 1 series airfoils with emphasis on maximizing laminar flow The airfoil is described using six digits in the following sequence The number 6 indicating the series One digit describing the distance of the minimum pressure area in tenths of the chord The subscript digit gives the range of lift coefficient in tenths above and below the design lift coefficient in which favorable pressure gradients exist on both surfaces A hyphen One digit describing the design lift coefficient in tenths Two digits describing the maximum thickness as percent of chord a followed by a decimal number describing the fraction of chord over which laminar flow is maintained a 1 is the default if no value is given For example the NACA 612 315 a 0 5 has the area of minimum pressure 10 of the chord back maintains low drag 0 2 above and below the lift coefficient of 0 3 has a maximum thickness of 15 of the chord and maintains laminar flow over 50 of the chord 7 series EditFurther advancement in maximizing laminar flow achieved by separately identifying the low pressure zones on upper and lower surfaces of the airfoil The airfoil is described by seven digits in the following sequence The number 7 indicating the series One digit describing the distance of the minimum pressure area on the upper surface in tenths of the chord One digit describing the distance of the minimum pressure area on the lower surface in tenths of the chord One letter referring to a standard profile from the earlier NACA series One digit describing the lift coefficient in tenths Two digits describing the maximum thickness as percent of chord For example the NACA 712A315 has the area of minimum pressure 10 of the chord back on the upper surface and 20 of the chord back on the lower surface uses the standard A profile has a lift coefficient of 0 3 and has a maximum thickness of 15 of the chord 8 series EditSupercritical airfoils designed to independently maximize laminar flow above and below the wing The numbering is identical to the 7 series airfoils except that the sequence begins with an 8 to identify the series See also EditNACA cowling NACA ductReferences Edit Allen Bob 31 January 2017 NACA Airfoils nasa gov NASA Retrieved 27 July 2020 E N Jacobs K E Ward amp R M Pinkerton NACA Report No 460 The characteristics of 78 related airfoil sections from tests in the variable density wind tunnel NACA 1933 Fundamentals of aerodynamics John D Anderson Jr third ed ch 4 a b Moran Jack 2003 An introduction to theoretical and computational aerodynamics Dover p 7 ISBN 0 486 42879 6 Aerospaceweb org Ask Us NACA Airfoil Series Payne Greg 8 Jul 1994 NACA 6 7 and 8 series archived from the original on April 27 2009 Gordon J Leishman Principles of Helicopter Aerodynamics p 361 Marzocca Pier The NACA airfoil series PDF Clarkson University Retrieved July 5 2016 E N Jacobs amp R M Pinkerton 1936 Test in the variable density wind tunnel of related airfoils having the maximum camber unusually far forward NACA Report No 537 a b Abbott Ira von Doenhoff Albert 1959 Theory of Wing Sections Including a Summary of Airfoil Data New York Dover Publications p 115 ISBN 978 0486605869 External links Edit Wikimedia Commons has media related to NACA 4 digit Airfoils UIUC Airfoil Coordinate Database coordinates for nearly 1 600 airfoils John Dreese s NACA airfoil coordinate generation program Works on Windows XP 7 and 8 NACA Airfoil Series NASA website feature on NACA airfoils Airfoil Interactive WebApp https engineeringjournals stmjournals in index php JoMA article view 3639 Retrieved from https en wikipedia org w index php title NACA airfoil amp oldid 1142043062, wikipedia, wiki, book, books, library,

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