Aerodynamic Fundamentals, Definitions and Aerofoils
3.8 Aerofoils
3.8.3 Groupings of Subsonic Aerofoils – NACA/NASA
From the early days, European countries and the United States undertook intensive research to generate better aerofoils to advance aircraft performance. By the 1920s, a wide variety of aerofoils appeared and consolidation was needed. Since the 1930s, NACA generated families of aerofoils benefiting from what was available in the market and beyond by further testing. It presented the aerofoil geometries and test results in a systematic manner, grouping them into family series. The generic pattern of the NACA aerofoil family is listed in [6] with well-calibrated wind tunnel results. The book was published in 1949 and has served aircraft designers (civil and military) for more than half a century and is still useful. The NACA was subsequently reorganised to the NASA and continued with aerofoil development, concentrating on having better laminar flow characteristics over an aerofoil. Also, the industry undertook research and development to generate better aerofoils for specific purposes, but they are kept ‘commercial in confidence’.
Designations of the NACA series of aerofoils are as follows: four-, five- and six-digit, given here are the ones of the interest to this book. Many fine aircraft have used the NACA aerofoil. However, brief comments on other types of aerofoil are also included.
The NACA four- and five-digit aerofoils were created by superimposing a simple camber-line shape with a thickness distribution that was obtained by fitting with the following polynomial [6]:
y= ± (t∕0.2) ×(
0.2969×x0.5−0.126×x−0.3537×x2+0.2843×x3−0.1015×x4)
(3.15) 3.8.3.1 NACA Four-Digit Aerofoil
Each of the four digits of the nomenclature represents a geometrical property, as explained here using the example of the NACA 2315 aerofoil, is shown in Figure 3.14.
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chord line Yc
Xc
leading edge
mean line
trailing edge parabola
parabola
Figure 3.14 Camber-line distribution of the NACA 2315.
Figure 3.15 Comparing NACA 0015, NACA 4412 and NACA 4415 geometries.
2 3 15
Maximum camber,ycas a percentage of chord
Location ofyc-maxin 1/10 of chord from the LE ratio as a percentage of chord
The last two digits give the maximum thickness to the chord
The camber line of four-digit aerofoil sections is defined by a parabola from the LE to the position of maxi- mum camber followed by another parabola to the TE (Figure 3.14). This constraint did not allow the aerofoil design to be adaptive. For example, it prevented generation of aerofoil with more curvature towards the LE in order to provide better pressure distribution. Figure 3.15 compares NACA 0015, NACA 4412 and NACA 4415 geometries.
3.8.3.2 NACA Five-Digit Aerofoil
After the four-digit sections came the five-digit sections. The first two and last two digits represent the same definitions as the four-digit NACA aerofoil and are still applicable except the camber shape differs as defined by the middle digit. The middle digit stands for the aft position of the mean line bringing the change in defining camber-line curvature. The middle digit has only two options of zero for a straight (i.e. standard) and one for an inverted cube. These are explained next for the NACA 23012 with NACA 23112 aerofoil.
2 3 0 or 1 12
Maximum camber as a percentage of chord,YC The design-lift coefficient is 3/2 of it, in tenths
Max. thickness of max camber in 1/20 of chordXC
0 – straight/standard 1 – inverted cube
The last two digits give the maximum thickness to chord ratio as a percentage of chord
Explanation for NACA 23012
First digit, 2. It has 0.02c maximum amount of camber with design-lift coefficient=2×(3/20)=0.3.
Second digit, 3. Position of maximum camber at 3×2/200=15% chord length from LE.
Third (middle) digit0. Aft camber shape is straight (standard).
Last two digits, 12. It has maximum thickness to chord ratio=0.12, i.e. 12% of the chord length.
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Aerodynamic Fundamentals, Definitions and Aerofoils 95
Figure 3.16 Comparison of an NACA 23012 aerofoil with NACA 23112 reflex aerofoils.
NACA 23112: Same as before, except that its aft camber shape has a inverted cube shape; that is, curved (NACA Report 537]. Figure 3.16 compares the NACA 23012 with the NACA 23112 aerofoil.
The NACA five series have been well used in many GA/utility category aerofoil. They have higherClmax, lowCm-acwith goodCdminandCl𝛼. However, these aerofoils are not suitable for ab nitio trainer aircraft due to abrupt stall characteristics that are not forgiving for student pilots.
3.8.3.3 NACA Six-Digit Aerofoil
The five-digit family was an improvement over the four-digit NACAseries aerofoil; however, researchers subsequently found better geometric definitions to represent a new family of a six-digit aerofoil. The state-of-the-art for a good aerofoil often follows reverse engineering – that is, it attempts to fit a cross-sectional shape to a given pressure distribution. The NACA six-digit series aerofoil came much later (it was first used for the P51 Mustang design in the late 1930s) from the need to generate a desired pressure distribution instead of being restricted to what the relatively simplistic four and five-digit NACA series could offer. The six-digit series aerofoils were generated from a more or less prescribed pressure distribution and were designed to achieve some laminar flow. This was achieved by placing the maximum thickness far back from the LE. Their low-speed characteristics behave like the four- and five-digit series but show much better high-speed characteristics. However, the drag bucket seen in wind tunnel test results may not show up in actual flight. Some six-digit aerofoils are more tolerant to production variation compared to typical five-digit aerofoils.
NACA six-digit aerofoils are possibly those most popular, widely used in various classes of aircraft. Their success was followed by increased effort to develop an aerofoil with laminar flow characterises over a wide speed regime. The definition for the NACA six-digit aerofoil example using NACA 632-212 is as follows.
An NACA six-digit aerofoil example 632-212 definition is:
6 3 Subscript2− 2 12
Six Series Location of min Cpin 1/10 chord
Half width of low drag bucket in 1/10 ofCl
IdealClin tenths (design)
Max thickness as a percentage of chord The six-digit aerofoil nomenclature follows the following sequence.
first number. The number ‘6’ indicating the series.
*second number. One digit describing the distance of the minimumcp(pressure) area in tens of percentage points of the chord.
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**third number. The subscript digit gives the range of lift coefficient in tenths above and below the design-lift coefficient in which favourable pressure gradients exist on both surfaces.
A hyphen in between.
fourth number. Ideal aerofoil design-lift coefficientClin tenths.
fifth and sixth numbers. The last two digits is the maximum thickness as a percentage of the chord.
*It does not refer to camber. In the complete form, the six series mean line type is indicated by an associated letter ‘a’ (p. 121 of [6]), not given here.
**The subscript can also be expressed in parentheses, for example 632-212 as 63(2)-212. Within the paren- theses there could be more numbers as explained in [6]. A modified aerofoil can carry the letter ‘A’ (e.g.
641A212 given in p. 122 of [6].
The nomenclature of NACA six series is an involved one. The readers are recommended to refer to [1]
(section 3.8 and p. 119–122) for the exact definition. This book only covers how to use the graphs of the extent applied in worked-out examples.
In the example of the six-series aerofoil NACA 652-415 given in Figure 3.17, the minimum pressure position is at the 50% chord location indicated by the second digit. This is the point of inflection at the upper surface.
The subscript 2 indicates that the minimum drag coefficient (drag bucket) is near its minimum value over a range ofClof 0.2 above and below the design-lift coefficient. The next digit indicates the design-lift coefficient of 0.4, and the last two digits indicate the maximum thickness in percentage of the chord of 15%.
Three NACA six-series aerofoils are compared with location of minimumCpfrom 0.3c to 0.5c from the LE.
3.8.3.4 NACA Seven-Digit Aerofoil
The seven-digit family of aerofoil followed to further maximising laminar flow achieved by separately identi- fying the low-pressure zones on upper and lower surfaces of the aerofoil. The aerofoil is described by seven digits in the following sequence (Figure 3.18).
first number. The number ‘7’ indicating the series.
second number. One digit describing the distance of the minimum pressure (Cp) area on the upper surface in tens of percent of the chord.
third number. One digit describing the distance of the minimum pressure area on the lower surface in tens of percent of the chord.
fourth is one letter referring to a standard profile from the earlier NACA series.
fifth number. Single digit describing the lift coefficient in tenths.
sixth and seventh number. The last two digits give the maximum thickness as a percentage of the chord.
Figure 3.18 is an example of the NACA 747A315 of the seven-digit aerofoil series. The first digit ‘7’ indicates the series number. The second digit ‘4’ signifies that it has favourable pressure gradient on the upper surface to the extent of 40% of chord peaking to minimumcpand thereafter starts the adverse pressure gradient. The third digit ‘7’ says the same for the lower surface and in this case up to 70%. The last three digits are same
NACA65(2)-415
max. thickness to chord ratio in tenth of chord ideal (design) CI in tenth
subscript (range of lift coeff. in tenth) location of min cp in tenth of chord 6 series nomenclature
0.9 1 0.8
0.6 0.7 0.5 0.4 0.3 0.2 0 0.1
NACA65(2)-415 (full line) NACA64(2)-415 (dashed line) NACA63(2)-415 (dash dot)
y axis
y axis
−0.05 0.05 0.1
0
Figure 3.17 Comparison of NACA652415, NACA642415 and NACA632415 aerofoils.
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Aerodynamic Fundamentals, Definitions and Aerofoils 97
Figure 3.18 The Seven Series NASA747A315 aerofoil.
nomenclature as for the six-digit NACA aerofoil, indicating it has a design-lift coefficient ofCl=0.3 and a maximum thickness of 15% of the chord, preceded by a letter ‘A’ to distinguish that it has a class of different sections.
3.8.3.5 NACA Eight-Digit Aerofoil
The NACA eight-digit aerofoil series are thesupercritical aerofoilsdesigned to independently maximise air- flow above and below the wing. These are a variation of the six-series and seven-series and the eight-digit series has the same numbering system as the seven-series aerofoils except that the first digit is an ‘8’ to identify the series. Application of NACA eight-digit aerofoils to aircraft is yet to be proven and not discussed here.
3.8.3.6 Peaky-Section Aerofoil
Peaky-section aerofoils were developed during the early 1960s by the large commercial aircraft manufacturers to fly at higherMcrit(20 count drag rise – see Section 3.14). It was done by tweaking their well-proven high performing aerofoil of the time by slightly drooping down the aerofoil nose section and re-contouring. This allowed a rise of local airspeed near the LE on account well designed nose droop, causing negativeCpto peak up, hence the name (Figure 3.19). Distributed weak local shocks were allowed to form at that area that do not cause flow separation until it may happen further downstream when higherMcritis reached.
1.6 0.2
0.4
0.6
0.8 1.0 T.E.
L.E.
Lower surface Upper surface Shock wave
Pressure ratio p/HO
M∞ = 0.73, CL = 0.77 Peaky design Conventional design
1.4 Local 1.2 Mach number1.0
0.8 0.6 0.4
x/c
Figure 3.19 Comparison between a peaky-section aerofoil with a conventional aerofoil.
k k The NASA supercritical aerofoil appeared during the mid-1960s and gradually replaced the peaky-section
aerofoil.
3.8.3.7 NASA Supercritical Aerofoil
In an effort to develop aerofoil to operate at a higher subsonic speed yet retaining good low-speed characteris- tics better than what existed, Richard T. Whitcomb of the Langley Research Center developed the supercritical aerofoil during the early 1960s. The goal was to increase the drag divergence Mach number (Figure 3.13), thereby reducing drag and allowing for more efficient flight in the transonic regime. It has the characteristic shape of a flat top following a large LE radius and curved tail with thickness at the TE.
This distinctive aerofoil shape helps the local supersonic flow with isentropic recompression on account of reduced curvature over the middle region of the upper surface and substantial aft camber.
The National Aeronautics and Space Administration (NASA) made systematic studies in three phases during the 1970s to develop this family of aerofoils with thicknesses from 2 to 18% and design-lift coefficients from 0 to 1.0. These were called the ‘supercritical aerofoils’.
Three phases of development are as follows:
Phase 1. Supercritical Aerofoils: Early Supercritical Aerofoils that increased the drag divergence Mach number beyond the six-series NACA family.
Phase 2. Supercritical Aerofoils: The extension of Phase 1 Supercritical Aerofoils with target pressure distributions.
Phase 3. Supercritical Aerofoils: aerofoils developed for studies to reduce Phase 2 LE radii. The study was eventually abandoned.
The supercritical aerofoil number designation is in the form in the example of SC(2)-0412 as shown in Figure 3.20. The aerofoil designation is broken down into two segments – the first segment of three charac- ters starts with SC, indicating it is a supercritical aerofoil and the bracketed number shows the development phase – in this case, Phase II of three phases of development as described next. The last segment starts with its first two digits as the design-lift coefficient in tenths and the last two are the thickness in percent chord, in the exampleCl=0.4 andt/c=12%.
3.8.3.8 Natural Laminar Flow (NLF) Aerofoil
The NLF class of aerofoil was designed by NASA during the early 1980s as a follow-up of the successful NACA six-series aerofoil for low subsonic speed GA aircraft operation offering low profile drag at high Re. NLF(1)-0213 and NLF(1)-0414 exhibited good laminar flow up to 70% of chord length at Mach 0.4 and Re=10×106. NLF type aerofoils suit the composite wing, that can have smooth polished surface, better than a metal wing.
the number indicates phase 2 development finite TE thickness
camber
cusp NASA SC(2) - 0412 Supercritical aerofoil
LE TE
Magnifi ed
0.9 1.0 0.8
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
x axis y axis −0.05
0.05 0
SC(2) - 0412
last two digits represent max t/c ratio in percent - 12%
the two digits represent design CI in tenth = 0.4 supercritical
Figure 3.20 Supercritical aerofoil NASA SC(2)-0412.
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Aerodynamic Fundamentals, Definitions and Aerofoils 99
Figure 3.21 Natural laminar flow aerofoil.
–1.0
Thicker leading edge
COMPARISON OF PRESSURE DISTRIBUTIONS OF NLF(1)-0414F & NACA 67-314
Optimization of acceleration
Concave pressure recovery
Cruise flap
NLF(1)-0414F ALP = 0.61 CMC/4 = –0.0849
CL = 0.46 M = 0.4 NACA 67-314 ALP = 0.80 CMC/4 = –0.0815
–0.5
0.5 1.0 1.5 0.0
Typically, NLF aerofoil shows ‘flat roof-top’ pressure distribution. NLF(1)-0414 has achievedClmax=1.83 at𝛼=18∘operating at Re=10×106. Figure 3.21 compares the NLF(1)-0414 with NACA 67-314.
Later for high-speed applications, for example, business jets, HSNLF(1) – 0213 was designed to suit appli- cations in compressible flow (HSNLF=high speed natural laminar flow aerofoil).
3.8.3.9 NACA GAW Aerofoil
The NASA General Aviation Wing (GAW) series evolved later for low-speed applications and use by GA (Figure 3.22). Although the series showed better lift-to-drag characteristics, their performance with flap deployment, tolerance to production variation and other issues are still in question. As a result, the GAW aerofoil has yet to compete with some of the older NACA aerofoil designs. However, a modified GAW aerofoil has appeared with improved characteristics.
The numbering system is similar to the supercritical aerofoil.
3.8.3.10 Supersonic Aerofoils
A supersonic aerofoil is a cross-section geometry designed to generate lift efficiently at supersonic speeds (Figure 3.23). The need for such a design arises when an aircraft is required to operate consistently in the supersonic flight regime. Supersonic aerofoils are necessarily thin in the range of≈0.04<(t/c)<≈0.07.
Supersonic aerofoils generally have a thin section formed of either angled planes (called ‘double wedge aero- foil’) or opposed arcs (called ‘biconvex aerofoil’) with very sharp leading and TEs. The sharp edges prevent the formation of a detached bow shock in front of the aerofoil as it moves through the air. This shape is in contrast to subsonic aerofoils, which often have rounded LEs to reduce flow separation over a wide range of angle of attack A rounded edge would behave as a blunt body in supersonic flight and thus would form a bow shock, which greatly increases wave drag. The aerofoils’ thickness, camber and angle of attack are varied to achieve a design that will cause a slight deviation in the direction of the surrounding airflow.
However, since a round LE decreases an aerofoil’s susceptibility to flow separation, a sharp LE implies that the aerofoil will be more sensitive to changes in angle of attack. Therefore, to increase lift at lower speeds,
0.05
–0.05 0 0
camber line
0.9 1.0 0.8
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
x axis
y axis
Figure 3.22 NASA/Langley/Whitcomb LS(2)-0413 (GA(W)-2) general aviation aerofoil.
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double wedge (sharp Leading edge) flat bottom wedge (sharp Leading edge)
hexagonal wedge (sharp Leading edge)
bi-convex (sharp Leading edge)
Blunt Leading edge Figure 3.23 Supersonic aerofoil.
aircraft that employ supersonic aerofoils also use high-lift devices such as LE and TE flaps. The thin six and seven series aerofoils have been used in combat aircraft design.
The supersonic aerofoil designation is as follows.
NACA NS− (X1)(Y1) − (X2)(Y2)
The letter ‘N’ is replaced by the series number, the number ‘1’ being used for wedge-shape profiles and the number ‘2’ being used for circular arc profiles. The letter ‘S’ denotes it is supersonic. The letter ‘X1’ represents the distance along the chord from the LE to the point of maximum thickness ‘Y1’ for the upper surface. The letters ‘X2’ and ‘Y2’ represent the corresponding values for the lower surface. ‘X’ and ‘Y’ are the percentage aerofoil cord length. In the following are some examples of 6%t/caerofoil.
Subsonic
NACA 66-006 blunt LE aerofoil
Supersonic
NACA 1S-(30)(03)-(30)(03) wedge shaped aerofoil (double wedge, max. thickness at 30% chord) NACA 1S-(70)(03)-(70)(03)
NACA 2S-(30)(03)-(30)(03)
NACA 2S-(50)(03)-(50)(03) circular arc aerofoil (in this case biconvex, max. thickness in middle) NACA.2S-(70)(03)-(70)(03)
Typically, the sharp LE thin supersonic aerofoil, at its clean basic configuration, has lowClmax(in the order of 0.8 to 0.9). Its LE droop increases the aerofoil camber givingΔClmaxin the order of 0.4 to 0.5. A 20∘ TE deflection can give nearly twice theClmaxof the basic aerofoilClmax.
3.8.3.11 Other Types of Subsonic Aerofoil
NACA’s earliest attempt (in the 1930s) to make a systemic generic type was the NACA 1-Series (or 16 series) [6]. This new approach to aerofoil design had its shape mathematically derived from the desired lift char- acteristics. Prior to this, aerofoil shapes were first created and then had their characteristics measured in a wind tunnel. The 1-series aerofoils are described by five digits. Since this type is no longer used, it is not discussed here.
Subsequently, after the six series sections, aerofoil design became more specialised with aerofoils designed for their particular application. In the mid-1960s, Whitcomb’s ‘supercritical’ aerofoil allowed flight with high critical Mach numbers (operating with compressibility effects, producing in wave drag) in the transonic region.
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Aerodynamic Fundamentals, Definitions and Aerofoils 101
The NACA seven and eight series were designed to improve some aerodynamic characteristics. In addition to the NACA aerofoil series, there are many other types of aerofoil in use.
To remain competitive, the major industrial companies generate their own aerofoil. One example is the peaky-section aerofoil that were popular during the 1960s and 1970s for the high-subsonic flight regime. Aero- foil designers generate their own purpose-built aerofoil with good transonic performance, good maximum lift capability, thick sections, low drag and so on – some are in the public domain but most are held commercial in confidence for strategic reasons of the organisations. Subsequently, more transonic supercritical aerofoils were developed, by both research organisations and academic institutions. One such baseline design in the United Kingdom is the RAE 2822 aerofoil section, whereas the CAST 7 evolved in Germany. It is suggested that readers examine various aerofoil designs.
There are many other types of aerofoil, for example, Eppler, Liebeck (used in gliders) and many older types, for example, the Wortmann, Gottingen, Clark Y, Royal Air Force (RAF) aerofoils and so on, not discussed here. There are large number of other aerofoil developed by many scientists, in addition to proprietary aerofoil developed by industry. However at this stage, the well-used and established NACA series aerofoils will serve adequately until the readers join industry to use their data and analyses methods, today using CFD. While, NACA series aerofoil test data are still prevalent, the use of DATCOM (the short name for the USAF Data Compendium for Stability and Control)/ Engineering Sciences Data Unit (ESDU) for aerofoil analyses is gradually receding. URLs [8–11] may prove useful to get some information on various types of aerofoil.
Discussion In earlier days, drawing the full-scale aerofoils of a large wing and their manufacture was not easy and great effort was required to maintain accuracy to an acceptable level; their manufacture was also not easy. Today, computer-aided drawing/computer-aided manufacture (CAD/CAM) and microprocessor-based numerically controlled lofters have made things simple and very accurate. In December 1996, NASA pub- lished a report outlining the theory behind the U.S. National Advisory Committee for Aeronautics (NACA) (predecessor of the present-day NASA) aerofoil sections and computer programs to generate the NACA aerofoil.
Aerofoil characteristics are sensitive to geometry and require hard tooling with tight manufacturing tolerances to manufacture to adhere closely to the profile.
Often, a wing design has several aerofoil sections varying along the wing span. Appendix F provides six types of aerofoil for use in this book. Readers should note that the 2D aerofoil wind tunnel test is conducted in restricted conditions and will need corrections for use in real aircraft. Section 3.14.1 gives a simplified aerofoil selection method.