AE 240 ‐ Handout No. 2 ‐ Airfoil Selection Guide Dr. Farooq Saeed 1. Airfoil Design or Airfoil Selection The two most common ways to determine the wing airfoil section are: (1) Airfoil design, and (2) Airfoil selection. The design of the airfoil is a complex and time consuming process and needs expertise in fundamentals of aerodynamics at graduate or post-graduate levels. Once a design is accomplished, it needs to be verified by testing it in a wind tunnel which is an expensive and timeconsuming process. Aircraft manufacturers such as Boeing and Airbus have sufficient human expertise (aerodynamicists) and budget to design their own airfoil for their aircraft. However, small aircraft companies, experimental and homebuilt aircraft manufacturers cannot afford to design their airfoils. Instead they select the best airfoils for their application from amongst a host of tried and tested airfoils that are found in literature, such as the NACA airfoil database. With the advent of high speed and powerful computers, the design of airfoil is not as hard as thirty years ago. There is currently a host of aerodynamic analysis and design software (XFOIL, PROFOIL, PROFIL, JavaFoil, etc.) in the market that can be used to design airfoil for a variety of needs. Airfoils are not only needed by aircraft designers but are also used in a host of other applications that include: jet engine axial compressor blades, jet engine axial turbine blades, steam power plant axial turbine blades, wind turbine propellers, centrifugal and axial pump impeller blades, turboprop engine propellers, centrifugal and axial compressor impeller blades and large and small fans, to name a few. The efficiencies of all of these industrial mechanical or aerospace devices depend mainly on the aerodynamic characteristics of the sectional profiles of their blades. If one has enough time, budget and manpower, and decides to design an airfoil for his aircraft, he should refer to the references that are listed at the end of this handout. But he should remember that the airfoil design is a design project by itself and needs to be integrated into the complete aircraft design process properly. But if one is a junior aircraft designer with limited resources, he is recommended to select the airfoil from the previously designed and published airfoil sections. Two reliable airfoil database resources are the NACA (Refs. 1 and 2) and Eppler (Ref. 3). These references contain airfoil coordinates, pressure distribution, lift curves (cl vs. ), drag polar (cd vs. cl), and moment coefficient plots (cm vs. ), for a range of Reynolds numbers. NACA airfoils use NACA designation while the Eppler airfoils use the letter “E” followed by three numbers. The choice of airfoil primarily depends on the critical segment of an aircraft’s mission profile. Typical mission segments include: take off, climb, cruise, turns, maneuvers, descent, approach, loiter and landing. For general aviation (GA) aircraft or commercial transports, the critical mission segment is the cruise segment, that is, the aircraft spends much of its flight time in this flight phase. The aerodynamic characteristics of the wing or its section, that is the “airfoil,” play a very important role during cruise since the aerodynamic efficiency of the wing (CL/CD) depends on the choice of airfoil. Thus, for an efficient cruise, the wing must produce sufficient lift while keeping drag to a minimum. For a steady, straight and level flight during cruise, the lift (L) must equal aircraft weight and drag (D) must equal engine thrust (T). Thus, the main governing equations for cruise are: 1 L W V 2 SCL mg 2 1 D T V 2 SCD nTmax (jet engine) 2 n P 1 D T V 2 SCD p max (prop engine) 2 VC (W), (1) (2) (3) Equation (2) is for an aircraft with jet engine while Equation (3) is for an aircraft with propeller engine. The variable “n” ranges between 0.6 to 0.9. It means that only a partial engine throttle Page 1 Since a major criterion for airfoil design is to satisfy cruising flight requirements. and the lift curve slope (ao or cl). i. 2 ‐ Airfoil Selection Guide Dr. This is essential for a cruising flight. since it leaves the capacity to have more lift at zero angle of attack. The stall speed (Vs) is inversely related to maximum lift coefficient. since the fuselage center line is aimed to be level (i. The variation of lift coefficient (cl) versus angle of attack () Figure 1 shows the typical variations of lift coefficient versus angle of attack for a positively cambered airfoil. the safer is the aircraft. thus the higher clmax leads to lower Vs and a safer flight. The design objective is to have a higher L=0 (more negative). AE 240 ‐ Handout No. thus a higher stall angle is sought in airfoil selection. when a high lift device is employed. This means that the pilot is not allowed to increase the angle of attack more than about 16 degrees.75. zero fuselage angle of attack) for variety of flight reasons such as comfort of passengers.e. aircraft weight). ideal or cruise lift coefficient (cli) and angle of attack corresponding to ideal lift coefficient known as wing setting angle (set). The maximum lift coefficient (clmax) is the maximum capacity of an airfoil to produce nondimensional lift. These features are critical to identify the performance of an airfoil. lift coefficient at zero angle of attack (cl0). the main airfoil characteristics and desirable qualities are described that can aid in the proper selection of airfoils for a particular application. since the aircraft will lose the balance of forces in a cruising flight. it is suggested to use 0. The significant features of this graph are: stall angle (s). iii. the capacity of an aircraft to lift a load (i. Typical values for L=0 are around –2 degrees when no high lift device is employed. If the stall is not controlled properly. The typical stall angles for majority of airfoils are between 12 to 16 degrees. In general. Figure 1. ii. Farooq Saeed is used in a cruising flight and maximum engine power or engine thrust is not employed. The maximum engine power or engine thrust is only used during take-off or when cruising with maximum speed. Equations (1) through (3) are used in airfoil design. the L=0 increases to about –12 degrees. a. The stall angle (s) is directly related to the flight safety. zero lift angle of attack (L=0). The exact value for n is determined in later design steps. However.e. such as 40 degrees of flap down. The zero lift angle of attack (L=0) is the airfoil angle of attack at which the lift coefficient is zero. In the sections that follow. the aircraft may enter a spin and eventually crash. Therefore the airfoil which has the higher stall angle is more desirable. maximum lift coefficient (clmax). the higher the stall angle. iv. In the initial stages of airfoil. A typical airfoil lift coefficient versus angle of attack curve and drag polar i.e. The ideal lift coefficient (cli) is the lift coefficient at which the drag coefficient does not vary Page 2 . since it implies we can produce more positive lift at zero angle of attack. The typical value of ideal lift coefficient for GA aircraft is about 0.01-0. Another important airfoil characteristic is the shape of the lift curve at and beyond the stall angle of attack (stall behavior). the design objective is to fly at the cruise lift coefficient that is as close as possible to the ideal lift coefficient. the more the cl0 the better it is. In general. since lower drag coefficient means lower flight cost (lower thrust and fuel consumption). The angle of attack corresponding to ideal lift coefficient is the wing setting angle (set).e.: cl cl1 ao cl 2 (4) 2 1 or one can also use the following empirical equation (approximate) in the absence of airfoil data: dc t (5) ao cl l 1. the fuselage angle of attack must be zero in cruise) and thus minimum fuel cost. The lift curve slope (ao or cl) is l another important performance feature of an airfoil. The ideal lift coefficient usually corresponds to the minimum drag coefficient. (2) produce minimum drag during cruising flight. since the pilot can recover more easily from a gradual drop in lift than a sharp one. rather than an abrupt or sharp loss of lift (see Figure 1). the wing setting angle in supersonic fighters. and in jet transports between 3 to 5 degrees. a careful wing Page 3 . An airfoil with a more gradual drop in lift past the stall is safer and hence desirable.1. Farooq Saeed significantly with the slight variations of angle of attack. It implies that for each 1 degree of change in the airfoil angle of attack. the higher the slope. and (3) be such that during cruise. curve.4. i.e. vii. the fuselage center line is parallel to the horizontal axis for passenger comfort and minimum drag (i.8 1 0.05. between 2 to 4 degrees. This is very critical in airfoil selection. The lift curve slope is the slope of variation of lift coefficient with respect to the change in the angle of attack. and its units are 1/deg or 1/rad. Although the sudden airfoil stall behavior does not necessarily imply sudden wing stall behavior. Figure 2.1-0. AE 240 ‐ Handout No. the better the airfoil. The lift coefficient at zero angle of attack (cl0) is the lift coefficient when the geometric angle of attack is zero. The wing incidence for majority of aircraft is between 0 to 4 degrees. and for supersonic aircraft 0. The wing setting angle is the angle between the wing chord line at root and the longitudinal axis (horizontal reference such as fuselage center line parallel to the cabin floor) as shown in Figure 2. Wing incidence or setting angle vi. v. From design point of view. Thus. Since the main function of an airfoil is to produce lift.8 max d c where tmax/c is the maximum thickness to chord ratio of the airfoil. in GA aircraft. 2 ‐ Airfoil Selection Guide Dr. The typical value of lift curve slope of an airfoil is around 2 (or 6. is between 0 to 1 degrees.28) per radian (or about 0. the lift coefficient will be increased by 0. The lift curve slope (1/rad) may be found from the lift curve data using the relation for a slope of a curve which in this case is the linear range of the cl vs.1 per degrees). viii. The wing setting angle must: (1) be able to generate the desired lift coefficient during cruising flight. It is also referred to as the wing incidence (iw) angle. The mid point of the bucket is the ideal or cruise lift coefficient (cli). As the drag is directly related to the flight (fuel) cost. the lift coefficient (drag polar) for a laminar airfoil Figure 3 shows a typical drag polar for a laminar airfoil. the best airfoils in this regard tend to have lower maximum lift coefficient.006. the pilot can bring the aircraft nose down (decrease the angle of attack) without being worried about an increase in the aircraft drag or constantly changing the throttle setting. the airfoil which has a lower cd min value is more desirable. AE 240 ‐ Handout No. cl curve. Page 4 . since it will cause the airfoil to pitch down if a gust of air results in an increase in its angle of attack (pitch up). Since the aircraft weight reduces as the fuel is burned during cruise.02 to -0. This graph has a unique feature called the drag bucket. The sign convention is that the moment is considered positive in the direction of pitch up or positive angle of attack. 2 ‐ Airfoil Selection Guide Dr. The unique aspect of the bucket is that the cd min is constant for a range of cl values. This is very significant. b.c/4 versus angle of attack is usually negative (nose-down moment) while the pitching moment coefficient about aerodynamic center cmac is almost constant. which means a heavier aircraft. This negative wing pitching moment must be balanced by the horizontal tail or stabilizer. Unfortunately. The lowest point of this graph is where the drag coefficient is minimum (cd min) and the corresponding lift coefficient is known as cl min drag. Farooq Saeed design can significantly modify the airfoil tendency to rapid stall. It is interesting to note that the pitching moment coefficient for a symmetrical airfoil section is zero (ideal for aerobatic aircrafts!!!). have a more gradual loss of lift. Therefore the airfoil which has the less negative cmac at the wing setting angle (set) corresponding to ideal lift coefficient is more desirable. A negative value of cm. a higher cmac (more negative) results in a larger tail. In general. usually about -0. Remember that the design lift coefficient occurs at the point whose cl/cd is maximum. since it implies that the pilot can stay at the lowest drag point for small changes in the angle of attack.003 to 0. Thus.c/4 or cmac is desirable. in which the separation is associated with the adverse gradient on the aft portion rather than the nose pressure peak. due to the bucket-like shape of the lower portion of the cd vs. A typical value for cd min is about 0. the slope of pitching moment coefficient about quarter-chord cm.05 for typical range angle of attacks. The variation of drag coefficient vs. The design objective for conventional aircraft is to have an airfoil with a negative cmac that is close to zero as much as possible. aircraft operate at cli yet at some other flight operations (such as loiter). while the highest cl in the bucket is referred to as the design lift coefficient (cl design). The variations of drag coefficient as a function of lift coefficient The cd vs. The variations of pitching moment coefficient versus angle of attack For a positively cambered airfoil. Figure 3. For some flight segments. The reason is that the aircraft must be in equilibrium during cruise. c. cl plot on the right in Figure 1 is called the drag polar and shows the typical variations of drag coefficient as a function of lift coefficient for a positively cambered airfoil. the objective is to fly at cl design. airfoils with thickness or camber. such as a 6-series NACA airfoil. A moderately thick airfoil is desirable since it can be structurally reinforced. vi. manufacturability. In general. A lower wing setting angle (set) corresponding to ideal lift coefficient (cli) that will result in a minimum drag which in turn would require minimum engine thrust (smaller engine) and hence minimize fuel consumption resulting in greater range. the following criteria should be used for the initial selection of an airfoil for a wing or aircraft. A less negative pitching moment coefficient about aerodynamic center cmac at the wing setting angle (set) corresponding to ideal lift coefficient is more desirable since it will reduce wing bending and torsional stresses. 2 ‐ Airfoil Selection Guide Dr. A lower minimum drag coefficient (cdo or cd min). The designer must also consider other requirements such as airworthiness. it is best to calculate the cl/cd ratio at several points on the drag polar near the tangent point. AE 240 ‐ Handout No. Both aircraft range and endurance can be maximized by maximizing the lift-to-drag ratio. An airfoil must be such that the cross section is easy to manufacture. Thus. a subsonic flight design requirements are very much different from a supersonic flight design objectives. The angle of attack corresponding to this point is an optimum candidate for a loitering flight (l). A proper ideal lift coefficient (cli) at which the drag coefficient is minimum and does notl vary significantly with slight variations of angle of attack. A more gradual or gentle stall is desirable since it is safer (easy of recovery) & will prevent spin. flight in the transonic region requires a special airfoil that meets drag divergence requirements. iii. if the fuel tank has Page 5 . For more accuracy. On the other hand. i. and cost requirements. vii. 2. xiv. ii. In general. Farooq Saeed d. The airfoil should not be very thin that spars cannot be placed inside. viii. Any other design and cost requirements must be considered. the typical values for the airfoil maximum thickness-to-chord ratio of majority of aircraft are about 6% to 18%. The variations of lift-to-drag ratio (cl/cd) as a function of angle of attack The last important parameter in the airfoil selection process is the variation of lift-to-drag ratio (cl/cd) as a function of angle of attack.. xiii. the typical wing t/cmax is about 6% – 9%. A higher maximum lift coefficient (cl max) is more desirable since it results in a lower stall speed (Vs) and thus a safer flight. Summary of Desirable Airfoil Characteristics for Airfoil Selection Selecting an airfoil is a part of the overall wing design process. Too much camber will result in an increase in manufacturing cost. A higher stall angle (s) is more desirable since it is safer. A higher maximum lift-to-drag ratio (L/Dmax or cl/cd max). For a low speed aircraft with a high lift requirement (such as cargo aircraft). Selection of an airfoil for a wing begins with the clear statement of the flight requirements. the maximum lift-to-drag point can be found by drawing a line tangent to the drag polar as shown in Figure 2. For the supersonic aircraft. Figures 1 & 2 show the points of maximum lift-to-drag ratio.e. iv. A higher lift curve slope (ao or cl) is desirable since it will result in higher lift or maximum lift coefficient x. v. For instance. e. The design objective is to fly at the cruise lift coefficient that is as close as possible to the ideal lift coefficient. xii. A higher zero lift angle of attack (L=0) (more negative) is more desirable since it leaves the capacity to have more lift at zero angle of attack as well as adds to passenger comfort. For instance. the typical wing t/cmax is about 15% – 18%. an airfoil with: i. the typical wing t/cmax is about 10% – 15%. a higher value of maximum lift-to-drag ratio is desirable. Airfoil maximum thickness-to-chord ratio (t/cmax) As a guide. For a high speed aircraft with a low lift requirement (such as high subsonic passenger aircraft). structural. horizontal tail size as well as control requirements xi. A higher lift coefficient at zero angle of attack (cl0). ix. the first digit indicates the maximum camber in percent chord. For example. Farooq Saeed been designated to be placed inside the wing inboard section. For example. the first digit gives the ideal lift coefficient of this airfoil as: (⅔)cli = 2/10 → cli = 2/10 × 3/2 = 0. the airfoil must allow the sufficient space for this purpose. and then a straight line connects the end point of the parabola to the trailing edge.and five-digit airfoil sections where designed simply by using parabolas and lines. The second digit indicates the position of maximum camber in tenths of chord length. c. A zero in the first digit means that this airfoil is a symmetrical airfoil section. Or if more than one airfoil is considered for a wing. The last two digits represent the maximum thickness-to-chord ratio. Four-digit NACA airfoils The four-digit NACA airfoil sections are the oldest and simplest NACA airfoils to generate. For example. Moreover. and has a maximum thickness (t/c)max = 8%. 1 5c o r 15% of the chord. you may find an airfoil that has the highest cl max. a. Five-digit NACA airfoils The camber of a five-digit airfoil section is made up of one parabola and one straight line. and another parabola produces the camber shape from the maximum camber to the trailing edge. the first digit represents 0. the second and third digits give the location of maximum camber as: 3 0 / 20 0 = 0 . It is an approximate representation of maximum camber in percent chord. 1 and 2). f o r the NACA 23012 airfoil section. Although these airfoils are easy to produce. there must be compromise through a weighting process. One parabola generates the camber geometry from the leading edge to the maximum camber. since not all design requirements have the same importance. such as laminar flow and no flow separation. 3. A zero in the first two digits means that this airfoil is a symmetrical airfoil section. but not the highest maximum lift-todrag ratio (cl/cd max). the maximum camber is located at 40% of the chord. The second & third digits indicate the location of maximum camber in two hundredths of chord length.15 or 2/3rd of ideal lift coefficient in tenths. new high-speed aircraft designs required more efficient airfoil Page 6 . In a five-digit NACA airfoil section. AE 240 ‐ Handout No. and the fourth and fifth digits give the maximum thickness (t/c)max = 12%. In a Four-digit NACA airfoil. The camber of a four-digit airfoil is made up of two parabolas. NACA Airfoils NACA (predecessor of NASA) developed one of the most reliable and widely used airfoil database resources in 1930s and 1940s. Details of the airfoils and the test are contained in (Refs. The 6-series NACA airfoils The four. 2 ‐ Airfoil Selection Guide Dr. It is stated here that there is no single airfoil will satisfy all of the above-mentioned requirements. The three most common and widely used types of NACA airfoils are the: Four-digit NACA airfoils Five-digit NACA airfoils 6-series NACA airfoils Some brief description of these airfoils is as follows: a. but they generate high drag compared to the other two airfoil categories. the NACA 1408 airfoil section has a maximum camber of 10%. In such cases. the integration of two airfoil sections in one wing must be smooth.3. The parabola generates the camber geometry from the leading edge to the maximum camber. They were not designed to satisfy major aerodynamic design requirements. The last two digits represent the maximum thickness-to-chord ratio. 4) and Lednicer (Ref. and the airfoil has 18% thickness-to-chord ratio (the last two digits).and five-digit airfoils. Table 2 lists the airfoil sections for several propeller-driven aircraft.006 0.4 1. For example.006 0. from Cessna GA (General Aviation) aircraft to F-16 fighter aircraft.013 -0.5 1. It demonstrates that the laminar bucket in the drag polar (cd vs. 5) and can be accessed online. NACA researchers developed several new series of airfoils that were driven by design requirements. Some 6-series airfoils have a subscript number after the second digit. it indicates the lift coefficient range in tenths above and below the value of ideal lift coefficient in which favorable pressure gradient and low drag exist. The 6-series NACA airfoils are designated by five main digits and begin with number 6.2 0.1 0. There is also a “-“ between the second digit and the third digit. Table 4 lists the wing incidence for several aircraft.55 1.05 -0. AE 240 ‐ Handout No.0052 0.0. More comprehensive lists of airfoil usage (what airfoils used on which aircraft) are maintained by Selig (Ref.25 1.4 1.6 (since 0.3 (the subscript) where the drag is minimum.1 0. The second digit represents the chord wise position of minimum pressure in tenths of chord for the basic symmetrical section at zero lift. The last two digits represent the maximum thickness-to-chord ratio. Table 3 lists the airfoil sections for several jet aircraft.0 -0.0048 9% 12% 15% 12% 15% 12% 15% 18% 10% 21% Page 7 . A zero in the third digit means that this airfoil is a symmetrical airfoil section. yielding lower values of cdmin compared to the four.008 -0.3 1.0 -0. Farooq Saeed sections.3 = 0.0052 0.5 0.042 -0. Amongst them the 6-series airfoils gained more interest since they were designed to maintain laminar flow over a large part of the chord. the first digit is always 6. Table 1 lists the characteristics of several NACA airfoil sections.4 1.2 0.1 -0. 2 ‐ Airfoil Selection Guide Dr.3 .1 s cmac (cl/cd)max cli cdmin (t/c)max (deg) 13 13 14 16 15 14 14 14 12 16 0.0045 0.3 + 0. Characteristics of several NACA airfoil sections No 1 2 3 4 5 6 7 8 9 10 Airfoil section 0009 4412 2415 23012 23015 631-212 632-015 632-618 64-210 654-221 clmax at Re=3×106 1.2 (the third digit).6 1. the NACA 633-218 airfoil section minimum pressure is located at 30% of the chord (the second digit). Note that all of the aircrafts listed in Tables 2 and 3. The third digit indicates the ideal lift coefficient in tenths. the lift coefficient range above and below the value of ideal lift coefficient is 0.0063 0. employ NACA airfoils. ideal lift coefficient of the airfoil is 0.0 0. cl curve) starts from a lift coefficient of 0 (since 0.004 0. In the 6-series airfoil designation.3 = 0) and ends at 0. Table 1.0065 0.0 0. To overcome this shortcoming.3 0.5 1. In case the airfoil name has a subscript after the second digit.025 39 71 86 60 52 67 61 52 57 46 0.005 0.09 -0.3 0. that is the series designation.6).4 0.004 0. AE 240 ‐ Handout No. Farooq Saeed Table 2.5% 15.5% 12% 2418 2412 15% 64A-109 9% 644-109 12% 641-212 641-212 63A-112 63A-309 10.3%) (10.8% 13% Transonic Transonic 5.1 282 Page 8 64A (6. 2 ‐ Airfoil Selection Guide Dr. 6) No Aircraft name 1 2 3 4 5 6 7 8 9 10 11 Cessna 550 Beech Bonanza Cessna 150 Piper Cherokee Dornier Do-27 Fokker F-27 Lockheed L100 PC-7 Hawker Siddely Beagle 206 Beech Super king First flight 1994 1945 1957 1960 1955 1955 1954 1978 1960 1967 1970 Max speed (knot) 275 127 106 132 145 227 297 270 225 140 294 12 13 14 15 16 Lockheed Orion Moony M20J Lockheed Hercules Thurston TA16 ATR 42 1958 1976 1951 1980 1981 411 175 315 152 269 17 AIRTECH CN-235 18 Fokker 50 1983 1987 228 282 Root airfoil 23014 23016.5% 15% 15% 15.5% 14.6%) 13.6%) 64A-204 64A-204 4% 18% 644-415 644-421 . The wing airfoil section of several jet aircraft (Ref.3%) Sonic rooftop Sonic rooftop 9.5 2412 652-415 23018 644-421 64A-318 642-415 23018 23015 2301823016.25% 11.2% 10.3% (10%) (8.8% airfoil airfoil (7.5 0014 632-215 64A318 642-A215 43 series (18%) 653-218 644-421 Tip airfoil 23012 23015 2412 652-415 23018 644-421 64A-412 641-415 4412 4412 23012 Average (t/c)max 13% 14.3% 0010 23012 Average (t/c)max 4.5% 0012 641-412 64A412 642-A215 43 series (13%) 653-218 644-415 13% 13.2% 0013 23014 64A (3%) 11.25% 12% 15% 18% 21% 15% 15% 15% 12.1990 31A Kawasaki T-4 1988 12 Gulfstream IV-SP 1985 13 Lockheed F-16 14 Fokker 50 1975 1985 Max speed Root airfoil Tip airfoil (knot) Mach 2.5% airfoil airfoil Supercritical Supercritical 8. The wing airfoil section of several prop-driven aircraft (Ref.5 468 275 441 333 360 383 595 1485 560 340 Mach 2.5% 18% 18% Table 3.8% 12. 6) No Aircraft name 1 2 3 4 5 6 7 8 9 10 11 First flight F-15E 1982 Beech Starship 1988 Lockheed L-300 1963 Cessna 500 Citation 1994 Bravo Cessna 318 1954 Gates Learjet 25 1969 Aero Commander 1963 Lockheed Jetstar 1957 Airbus 310 1982 Rockwell/DASA X. 1067 1. cli.2 0. s (deg). Aircraft Type Jet transport Prop-driven transport Wing Incidence 5o 30’ 3o 30’ Cruising Speed (Knot) Mach 0. AE 240 ‐ Handout No. L=0 (deg). cd min. and t/cmax of the NACA 63-209 airfoil section (flap-up) at a Re = 6 × 106 (or 6 million). correspond to wing setting angle set.5 cli cd min cmac 0. 2. cd min and cmac.35 272 5 6 7 8 9 Tucano Antonov An-26 BAE Jetstream 31 BAE Harrier Lockheed P-3C Orion Turbo-Prop Trainer Turbo-prop Transport Turbo-prop Business V/STOL close support Prop-driven transport 1o 25’ 3o 3o 1o 45’ 3o 222 235 282 570 328 10 11 Rockwell/NASA X-31A Kawasaki Jet combat research Prop-driven transport 0o 0o 1485 560 12 ATR 42 Prop-driven transport 2o 265 Turbo-prop Transport Turbo-prop Transport Jet transport Jet transport Jet fighter o 13 14 15 16 17 Beech Super King Air B200 SAAB 340B AVRO RJ McDonnell MD-11 F-15J Eagle 3 48’ 2o 3o 6’ 5o 51’ 0o 289 250 412 Mach 0. and clo corresponds to = 0 deg. cmac. 6) No.design.5 Example 1 Identify set (deg). 2 ‐ Airfoil Selection Guide Dr. page 419 and attached as Figure 4.0 cl.8-0)/ (6-(-1. Wing setting or incidence angle for several aircraft (Ref.5 = 75 clo 1. cl max. As an exercise. Farooq Saeed Table 4.005 -1.375/0. cl. correspond to angle for loiter conditions l. clo. The aerodynamic characteristics of the airfoil can be found in Ref. cl.45 s (deg) 12.5 cl max ao = cl t/cmax (0.0045 -0. ao = cl(1/rad).375 0.033 l (deg) 2.5)) = 0. Solution: By referring to Figure 4. the required values for all parameters at Re = 6 million ( symbols) are as follows: set (deg) 0.8 282 1 2 Airbus 310 Fokker 50 3 4 Sukhoi Su-27 Embraer FMB-120 Brasilia Jet fighter Prop-driven transport 0o 2o Mach 2. Page 9 .45 per deg = 6.design (cl/cd)max L=0 (deg) 0. (cl/cd)max.design and (cl/cd)max. indicate the locations of all parameters on the airfoil characteristics plot in Figure 4.1115 per rad 9% Note: cli.87 > Mach 2. Farooq Saeed Figure 4. Page 10 . 1). 2 ‐ Airfoil Selection Guide Dr. Aerodynamic characteristics of the NACA 63-209 airfoil section (Ref. AE 240 ‐ Handout No. and are the air density and viscosity. 2 ‐ Airfoil Selection Guide Dr. In the conceptual design phase where the wing geometry has not been designed yet. 3. otherwise estimate the weight of the aircraft (Wave) from historical data on similar aircraft. It is assumed that an airfoil section data base (Refs. the wing cruise lift coefficient (CLcw) can be approximated by: CL (8) C Lcw c 0. dihedral. etc. etc. this approximate relation must be modified to account for changes in the wing geometry by using appropriate aerodynamic analysis & design software tools. sweep. This may further be affected by factors such as wing taper. at cruise altitude. With this initial information. Calculate the airfoil ideal cruise lift coefficient (cli). In later design iterations. so: 2Wave Vc c 2 1 2 (7) . one proceeds towards the conceptual design phase where the first step is to design a wing with select airfoil sections that will support the weight of the aircraft yet at the same time offer minimum possible drag. In the initial preliminary design stage. Since other aircraft components may contribute to the total aircraft lift. Farooq Saeed 4.95 Later in the design. Page 11 . the general characteristics of an airfoil section. Practical Steps for Wing Airfoil Section Selection In the previous sections. weight. the average aircraft weight in cruise must be considered. That is. the practical steps for wing airfoil section selection are presented. In this section. L = W. and criteria for airfoil section are covered. 4. this relationship is updated. when other components have been identified and defined in subsequent design iterations. With this objective in mind. the following approximate relation is recommended: CL (9) c l i cw 0. Calculate the wing ideal cruise lift coefficient (CLcw).: 1 (6) Wave Wi W f 2 where Wi is the initial aircraft weight at the beginning of the cruise and Wf is the final aircraft weight at the end of the cruise. i. respectively. and S is the wing planform (reference) area. the selection of an appropriate airfoil section can be accomplished by following the steps outlined below: 1.e. AE 240 ‐ Handout No. Unless given. It is also assumed that the aircraft designer has the initial geometric and performance specifications of the aircraft based on data from historical trends and existing similar aircraft. negatively or positively. cruise conditions. the designer has a good idea about the wing dimensions. Calculate the aircraft ideal cruise lift coefficient (CLc) and the associated Reynolds number Re based on the mean aerodynamic chord c . The wing is a three-dimensional body with a finite span and is subject to induced flow effects due to the downwash created by the wing tip vortices. 1 through 3) is available and the wing designer is planning to select the best airfoil from the list.9 Later in the design. Re and MAC CLc c cr 3 1 Vc2 S where Vc is the aircraft cruise speed. the wing lift may be different than the aircraft lift. 2. In cruise. NACA airfoil sections. The result is a decrease in the wing lift coefficient. A typical comparison table which includes a typical weight for each design requirement is shown in Table 5. By reducing the wing t/cmax to 6 and 4 percent. 2 ‐ Airfoil Selection Guide Dr. Among several acceptable alternatives. 6. only a rough estimate of the high lift device contribution (CL. For a preliminary estimate.21 of text or airfoil data with split flap in Refs. 10. refer to Refs. HDL 8. If the wing is designed for a high subsonic passenger aircraft. At take-off. Every black circle represents one NACA airfoil section. The reason is to reduce the critical Mach number (Mcr) and the drag-divergent Mach number (Mdd). 1 and 2. Reference 9 is a rich resource for the systematic procedure of the selection technique and table construction. 1 & 2. the magnitude of the drag rise is progressively reduced. If there is no airfoil section that delivers the desired cli and clmax. a thinner airfoil will yield a higher Mcr than a thicker airfoil (Ref. Select a high lift device (type. At this stage of design.. Note: The split flap data (cl and cd) in Refs. The horizontal axis represents the airfoil ideal lift coefficient while the vertical axis the airfoil maximum lift coefficient. the wing is producing maximum lift while operating close to its stall speed Vs..2Vs. i. i.e.05 (Ref. Figure 6 shows the variation of the drag coefficient versus Mach number for three airfoil thickness ratios where the Mdd of the 9% percent thick wing occurs at about 0.e.88. 8). Page 12 . This can be found from the following relation: CL (11) clmax gross max TO 0.95 0VTO2 S and Re 0VTO c 0 (10) where and are the air density and viscosity. and maximum deflection).HLD) to the airfoil "gross" maximum lift coefficient should be made. 1 and 2 is given at different Re and for 60o flap deflection. For cli and clmax of other airfoil sections. Identify airfoil section alternatives that deliver the desired cli (step 4) and clmax (step 8). 8). 7). select the airfoil section that is nearest to the design point (desired cli and clmax). and WTO is the aircraft maximum/gross take-off weight. 7. Calculate the wing maximum lift coefficient at takeoff (CLmax TO) and the associated Reynolds number Re based on the mean aerodynamic chord c .g. respectively. the Mach number at which the slope of the CD versus M curve is 0. flap) is included. Thus: CLmax TO 2WTO 0. the takeoff speed VTO = 1. In general. select the optimum airfoil by using a comparison table. and the value of Mdd is increased. Figure 5 shows a collection of cli and clmax for several NACA airfoil sections in just one graph (Ref. AE 240 ‐ Handout No. geometry. moving closer to Mach one. use data of Figure 1. 9. Repeat steps 3 & 4 to obtain the airfoil “gross” maximum lift coefficient (clmax). Farooq Saeed 5. This is a very essential step. select the thinnest airfoil (the lowest t/cmax). This allows the aircraft to fly closer to Mach one before the drag rise is encountered. The choice of flap deflection is dictated by the fact that the wing airfoil “net” maximum lift coefficient as follows: (12) clmax clmax gross C L .9 where the airfoil “gross” maximum lift coefficient is the airfoil maximum lift coefficient in which the effect of high lift device (e. at take-off altitude (usually sea level). The data for any other flap deflection can be found by linear interpolation between clean and 60o-flap data. AE 240 ‐ Handout No. Variation in maximum lift coefficient for various airfoil section ideal lift coefficients (Ref. 7) Page 13 . 2 ‐ Airfoil Selection Guide Dr. Farooq Saeed Figure 5. 9091 (250 0.4(287 J/kg-K)(4.15) CLcw CLc 0.8 million 1.81 0. The high lift device (split flap) will provide CL. Variation of wing drag coefficient versus Mach number with airfoil thickness ratio as a parameter (Ref.HLD = 0.9091 (250 0.694 10 5 M= Vc Vc 250 0.95 CL 0.2 0. AE 240 ‐ Handout No.39 a RT 1.95 Page 14 .174 0. 2 ‐ Airfoil Selection Guide Dr.183 0. and c 1 m .9 0.183 cli cw 0. A sample table to compare the features of five airfoil sections Weight Airfoil 1 Design objectives cdmin cmac Airfoil 2 Airfoil 3 Airfoil 4 Airfoil 5 25% 15% 15% s L=0 10% (cl/cd)max ao or cl Stall quality Total 10% 5% 20% 100% 64 76 93 68 68 Example 2 Select a NACA airfoil section for the wing of a jet non-maneuverable GA aircraft with the following characteristics: mTO = 4000 kg.204 cli 0.5144 0.9 0.5o C 273. Farooq Saeed Figure 6. Table 5. S = 30 m2.4 when deflected.5144) 1 6.5144) 2 30 Re Vc c 0. Vc = 250 knot (at 3000 m). Vs = 65 knot (sea level). 8).174 2 Vc S 0. The wing is swept where the sweep angle is 47 degrees. Solution: Ideal (cruise) lift coefficient: CLc 2Wave 2 4000 9. 1410. and 662-215 Next. 2415.. 642-215. 631-212. the airfoils with sharp stall characteristics include: NACA 63-210. and 661-212. 641-212.e.552 0.9 0. 642A215. we need to look for NACA airfoil sections that have an ideal lift coefficient of 0. 642-015. NACA 0012. Farooq Saeed Maximum lift coefficient: 2WTO 2 4000 9. 652-215. and 662-215 Once the choice of candidate airfoils is reduced to a short-list (5-7 airfoils). since it is a jet aircraft (subsonic M = 0.2 cl max gross cl max C Lmax TO Thus. 63A210. 66-210. 63A210. 632-015. cli = 0. 661-212.2.2.552 0. 641A212. 652-215. 64A210. As a first step.2) just past the maximum lift coefficient point. 2415.e and Table 3 suggest that the maximum airfoil thickness should be between 10% – 15%.2 cli + cli within the minimum drag bucket) and a net maximum lift coefficient of equal or greater than 1. 631-212. 632-415. the last two digits should be between 10 or 15 for NACA 5-digit or 6-series airfoils. 2410. 632-015. 651-212. Thus.005.2 65 0. The remaining candidate airfoils are: NACA 641-112.75 3 million 1.5144) 1 2. and 10% t/cmax 15%: NACA 66-210. 651-212. 641-112.3963 2 0. Although the sudden airfoil stall behavior does not necessarily imply sudden wing stall behavior.e. In almost 99% of the design cases.95 0VTO S 0. 642-015.152 cl max 1. 2 ‐ Airfoil Selection Guide Dr. a lower value of minimum drag coefficient cd min is desirable at or near the ideal lift coefficient. Page 15 . 64A210. 1410. look up the airfoils listed in References [1] and [2]. 652-215. The remaining candidate airfoils are: NACA 63-210.3963 1.5144) 2 30 ReTO 0VTO c 1. we eliminate airfoils with very sharp stall characteristics.81 CLmax TO 1. and 662-215 In order to select an airfoil from amongst these candidate airfoils.2 65 0. 23015. which are excluded from the previous list. In this exercise. AE 240 ‐ Handout No. 2412. from Figure 5. i. 661-212. 4415. 641-212. 4415. For more or better choices. 65-210. 651-212.2. 65-210. 642-215. section 1. cl max 1. 641A212.225 (1. we eliminate all that have a cd min 0. 64-210.4 1. Reference [2] lists the following additional airfoils that satisfy the design requirements: NACA 0012. 64A210. a table should be drawn that lists important aerodynamic characteristics of the airfoils to facilitate comparison and help identify which airfoil is the best as demonstrated in Table 6.39). 641-212. Moreover. 642-015.e. 642-215.e. 642-A215. 4412.. 66-210. i.95 1. 632-415 and 632-215. i.. 64-210. 1412. 2412. we find the following airfoils whose characteristics are close to the design requirements. 641-112. 23015. a careful wing design can significantly modify the airfoil sharp stall tendency. 63A210. 64210. 641A212. 65-210. 4412.9 cl max gross CLHLD 1.2 (or an airfoil with cli 0. 1412. 642A215. i.789 105 0 1.225 (1. 632-215 Please note that Figure 5 lists a limited number of airfoils. 631-212. For this example. we follow a process of elimination. 63-210. 2410. the lift curve drops off sharply (almost vertical or within 2 degrees angle of attack for a cl = 0. 642A215. .50 1.0035 -0. decrease wing lift coefficient or slow down the aircraft.5 1.4 60 83.5 89 104 108 Moderate Moderate Moderate Docile Moderate Moderate Moderate Moderate -12 -12 -12 -13 -13 -13. when there is no clear choice of airfoil.45 1. i. iii. the selection may be further refined by using a comparison table. such as Table 4.0045 0.42 1. During cruise. Thus. ii.33 1. second to best safest flight as well as lowest control problem in flight and is. Page 16 . 2 ‐ Airfoil Selection Guide Dr. By comparing the numbers in the above table.5 -13 -13. to avoid higher drag at lower than ideal lift coefficient.48 1. the wing setting angle should be chosen considering the changes in lift coefficient at the start and end of cruise segments. The NACA 662-215 airfoil section delivers the highest maximum speed. the cd min is the lowest. iv.45 The best airfoil is the airfoil whose cmac is negative and closest to zero.39 1.035 -0. The NACA 662-215 airfoil section yields the highest maximum speed. In cases.5).028 14 16 15. ii. since it has the highest cl max (1.5 15. since it has the lowest cd min (0. Since a constant lift is maintained by the wing. incorporating the weighted design requirements. Some Observations: i. The NACA 641-212 airfoil section delivers the lowest control problem in flight.027 0. clearly the best choice for the design. due to docile stall quality. the s is the highest.0046 0.3 93.021 -0.0047 0.e. you can choose any airfoil with a cl max value equal or greater than the required value but not less than it. In fact both are almost same and by same authors. AE 240 ‐ Handout No. the stall quality cannot be sharp.0043 0. highest endurance. During selection. therefore. A comparison among five airfoil candidates for use in the wing of Example 2 No NACA cd min cmac s (deg) 0L (deg) cl max at Flap up f = 60o ReTO (cl /cd)max Stall quality 1 2 3 4 5 6 7 8 641-112 641-212 642-015 642-215 641A212 642A215 652-215 662-215 0. iii. The NACA 662-215 airfoil section yields the highest endurance. 2). the pilot must either lower the wing angle of attack. since it has the highest (cl /cd)max (111). The NACA 642-215 airfoil section yields the safest flight. due to the lowest cmac (-0.027).039 -0. to maintain constant altitude.0035). the (cl /cd)max is the highest.0044 0.033 -0.0047 0. the aircraft altitude will continue to increase due to decrease in its weight. The NACA 641-212 airfoil section yields the lowest stall speed. It is sometimes more preferable to have wider drag bucket both for the above reason and to be safe from higher drag coefficient values that could be encountered during gusts as a result of sudden changes in wing angle of attack. and the stall quality is docile.030 -0. Thus.5 14 16 16 17 65 81. In this exercise.000 -0. the final choice of airfoil was quite obvious. we can conclude the followings: i. v. Since the aircraft is a non-maneuverable GA aircraft.0044 0. 1) or the book by Abbot and Von Doenhoff (Ref. the aircraft weight decreases as the fuel is consumed. Farooq Saeed Table 6. hence airfoils with sharp stall are not acceptable. And this is only database discussed in class as far as airfoil selection is concerned.34 1. The NACA database refers to the NACA report 824 (Ref. David .raphael.edu/m-selig/ads. in the NACA database. Richard. 5.html) Martin Hepperle’s Site (www. Airfoil Comparison and more (http://airfoiltools.edu/xfoil/index. 2003. Blanchard B. For the handout example. Abbot. Louis Jr. use linear interpolation between the data for clean and flapped cases.ae. Third Edition. 9. Prentice Hall. Lednicer. and Stivers.edu/m-selig/ads.ae. Shevell R.html).htm). 6.. Abbott.. and Von Doenhoff. McGraw-Hill. and Fabrycky W. Stall characteristics: Docile or Gentle Moderate Sharp or Abrupt References: 1. During airfoil selection. Anderson John D. and A.illinois. Jane’s All the World’s Aircraft.illinois. Jane's information Group. Third edition. what airfoil(s) are used in the wing of a particular aircraft (www. Eppler. Airfoil Design and Data. Systems Engineering and Analysis. Moreover. Various years.ae. Jackson P. Prentice Hall. H. 3. E.. 7. 5. Dover. AE 240 ‐ Handout No.html) Kel Comp (www. NACA Report 824.mit..edu/m-selig/ads/aircraft. the maximum flap deflection was set to 20 deg. Thus to get the lift characteristics for the 20 deg flap deflection.html) The Incomplete Guide to Airfoil Usage (www. Fundamentals of Flight.com/compare/index) XFOIL (www. Selig. 1990 4. Summary of Airfoil Data.html). Albert E. Second edition. UIUC Airfoil Data Site (www. S.mh-aerotools.com/~kelcomp/) Page 17 . 6. Von Doenhoff. the flap characteristics are for 60 deg flap deflection.. New York 1959. v.ae. 2.illinois. Theory of Wing Sections. 1989. 2006. Ira H. The Incomplete Guide to Airfoil Usage.. Springer-Verlag. UIUC Airfoil Data Site (www. make sure that its flap characteristics (cl and cd curves for deflected flap) are given. 8.de/airfoils/index. 4.illinois.ctaz. (A MUST-HAVE BOOK for all aerospace engineers!!!) 3. References 1 or 2 provide split flap characteristics for some of the airfoils. Farooq Saeed iv. Modern Compressible Flow. (Available on Blackboard) 2.. 2 ‐ Airfoil Selection Guide Dr. Useful Links: 1. I. 1945.. Berlin. For takeoff you can limit flap deflection to any value between 10 and 60 deg based on your requirements. M. S. J.edu/m-selig/ads/aircraft. S. Publications.