5. WING AND TAILPLANE DESIGN

5.1 Maximum Lift Coefficient The maximum lift coefficient of the airplane CL,max depends upon many factors. Only the most important of these will be considered in this study and they are listed below.

a) Airfoil maximum lift coefficient cl,max : b) Wing aspect ratio, taper ratio and sweepback angle.c) Trailing edge flap design and deflection angle.d) Leading edge flap design and deflection angle.

The methods to be used to estimate CL,max for the various configurations of a wing are found in the USAF Stability and Control DATCOM (Ref. 5-1) the appropriate sections of which are reproduced in the Appendices to this handbook The material presented below directs the reader to the appropriate sections where the pertinent data may be found, and summarizes the procedure.

The airfoil sections to be considered will be those of the NACA four and five digit airfoils along with the 6-series laminar flow airfoils. These are described in Abbot, et al (Ref. 5-2) and in the book by Abbott and von Doenhoff (Ref. 5-3), as well as in DATCOM (Ref. 5-1) and given here in Appendix A. The characteristics of wing planforms and the definitions associated with them are given in DATCOM (Ref. 5-1) and are presented in Appendix B.

There was a resurgence of airfoil development in the 1960s and 1970s following a long hiatus in the two decades following the Second World War. NASA launched a concerted effort to develop new airfoil sections that would have improved performance at high subsonic Mach numbers. In particular, designs were sought that would delay the drag divergence Mach number and maintain reasonable drag coefficients at the turbulent flow conditions typical of high speed flight while retaining acceptable maximum lift and stall characteristics at the low speeds typical of landing. This research led to the so-called supercritical airfoil, one that has a distinctive shape compared to standard airfoils. A description of these developments is given by Harris (Ref. 5-4). Airframe manufacturers are also actively engaged in this work, but their results are proprietary, and hence unavailable. Newly developed NASA airfoils are described in a number of reports not readily available outside of the aerospace industry. McCormick (Ref. 5-5) also describes some of the newer airfoils. However, no other single report exists which collects and summarizes a wide range of NACA airfoil results as does Ref. 5-2. For these reasons, and for reasons of expediency, it is suggested that NACA airfoils be used.

5.2 Wings at Angle of Attack A great deal of theoretical and experimental work has been done toward the development of airfoil sections. Theoretical airfoil design is hampered by the existence of viscous effects in the form of a "boundary layer" of low-energy air between the airfoil surface and

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the free stream. This boundary layer affects chiefly the section drag and maximum lift characteristics but also has minor effects on lift-curve slope, angle of attack for zero lift, and section pitching-moment coefficient.

Since the boundary layer is influenced by surface roughness, surface curvature, pressure gradient, heat transfer between the surface and the boundary layer, and viscous interaction with the free stream it is apparent that no simple theoretical considerations can accurately predict all the airfoil characteristics. For these reasons, experimental data are always preferable to theoretical calculations. Airfoils have been optimized for many specific characteristics, including: high maximum lift, low drag at low lift coefficients, low drag at high lift coefficients, low pitching moments, low drag in the transonic region, and favorable lift characteristics beyond the critical Mach number. Optimization of an airfoil in one direction usually compromises it in another. Thus, low-drag airfoils have poor high-lift characteristics, and high-lift airfoils have low critical Mach numbers.

It is apparent from the above that any generalized charts for airfoil section characteristics, including the ones in this handbook, must be used with caution. Included in Appendix C are tabulated NACA experimental and theoretical data presented in DATCOM (Ref. 5-1). Table 4.1.1-A of Appendix C summarizes experimental data for the NACA four- and five-digit airfoils. Table 4.1.1-B gives corresponding data for the NACA 6-series airfoils. The data are for smooth leading-edge conditions and 9 x 106 Reynolds number.

Information is presented in those tables on the following airfoil characteristics:

1. Angle of attack at zero lift, 0

2. Moment coefficient at zero lift, cm,0

3. Lift-curve slope, cl,

4. Aerodynamic center location in percent chord, a.c.5. Angle of attack for maximum lift coefficient,

6. Maximum lift coefficient, 7. Angle of attack at which the lift curve deviates from linear

variation, a0

From these first five quantities the approximate section lift-curve shape can be synthesized, as illustrated in Fig. 5-1.

5.3 Airfoil Selection The airfoil selected for your design depends upon the cruising speed which in turn is related to the powerplant chosen. If the selected powerplant is a turboprop the speed range for cruise will be in the range of 250 to 350 mph. The average wing/airfoil thickness ratio can be from 13 to 15% for such aircraft. A larger thickness ratio is generally chosen for the root chord than for the tip chord, in order to provide a deep section at the root to reduce the bending stresses acting there. The tip chord thickness ratio is made smaller to provide an average value which optimizes cl,max, and typically lies in the range of 13% to 15%.

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Figure 5-1 Schematic diagram showing the five elements of the airfoil lift curve

It is recommended that the airfoil selected be chosen both on the value of cl,max and upon the post stall variation of cl with angle of attack. An abrupt drop in section lift coefficient is to be avoided, and the airfoil with the smallest decrease in cl for angles of attack above the stall is highly desirable, even at the expense of a smaller value of cl,max. In the 1930's and 40's designers chose wings which used the NACA 2412 at the root and the 4412 at the tip. The NACA 23012 or 23015 airfoils have higher maximum lift but these airfoils exhibit a large loss in cl beyond the stall. The NACA 6-series have smaller leading edge radii than the 4- and 5- digit series and the maximum thickness moves aft as the second digit of the 6-series increases. The maximum thickness of the 4- and 5-digit airfoils is at 30% chord. The position of the maximum thickness of the 63, 64 and 65 series is located progressively aft. The 63 series airfoils might be considered for the turboprop aircraft. The NACA 63-215 is a suggested airfoil section because of its favorable stall characteristics. It is advisable to investigate those airfoil sections used by the competition (market survey aircraft) as justification for your choice of airfoil.

The turbofan aircraft will typically cruise at high subsonic Mach number, typically in the range of 0.74<Mcruise<0.80. The upper limit chosen is to avoid the drag rise associated with the transonic speed regime. The average wing thickness will be in the 9% to 12% range, the lower value associated with relatively unswept wings and the higher value with the moderately swept (c/4 > 35o) wings. The NACA 64-2xx or the 64-4xx series airfoils might prove satisfactory for these aircraft. Again it is suggested that your market survey be utilized to glean information. As mentioned previously in Chapter 2, the range of thickness-to-chord ratio, t/c, for commercial airliners lies in the range 1.63A< t/c <2.25A, where t/c is measured in %.

In order to facilitate the airfoil selection process the pertinent sections of DATCOM (Ref. 5-1) are presented in the Appendices A and C and are presented below with comments. The stall characteristics of airfoils have been correlated in by an airfoil height parameter

cl

,a

0 0 0cl,max

cl

cl,max

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y which is shown in Fig. 2.2.1-8 in Appendix A. The value of y naturally increases (linearly) with airfoil thickness ratio and depends upon the NACA airfoil family.

A summary of cl characteristics of various airfoils is given in Tables 4.1.1-1A and 4.1.1.-1B of Appendix C. Included are values of 0, cm,0, cl,, xac /c, cl,max, cl,max and 0, where 0

is the angle of attack at which the cl vs curve deviates from a straight line. The values of cm,0 are observed to increase significantly with the design lift coefficient (the third digit in the 6-series airfoil) and these large negative values are to be avoided in the high speed designs because they tend to put the aircraft in a dive and/or twist the wing to negative angles of attack. A design lift coefficient of 0.2 is preferred to one of 0.4 for this reason. Appendix C (Section 4.1 of Ref. 5-1) need not be used alone for airfoil selection purposes; Refs. 2 and 3 may also be consulted.

The airfoil selection must be made before proceeding further and the value of cl,max

corresponding to M = 0.2, Re,c = 9 x 106, and standard roughness noted. On the basis of your market survey you should also select the wing aspect ratio A, the taper ratio , and the sweepback angle of the quarter chord line c/4. The following guidelines are suggested:

Engine speed in cruise c/4 A Turboprop V=300 mph 0o 0.5 7 to 11Turbofan M=0.8 25o to 35o 0.33 6 to 9

5.4 Compressibility Effects on Airfoils Consider a typical airfoil, the NASA 642-015, a symmetric section with 15% thickness. The theoretical inviscid surface velocity distribution is shown in Fig. 5-2 (Refs. 5-2 and 5-3). Two distributions are illustrated, one for zero angle of attack where cl =0, and one for moderate angle of attack where cl =0.22. Because the section is symmetric the zero angle of attack case has exactly the same velocity distribution on both the upper and lower surfaces. As a result the pressure distributions are also identical on both surfaces and therefore the net lift is also zero. However, in the moderate angle of attack case the upper surface of the airfoil has a consistently higher velocity on the upper than on the lower surface resulting in lower pressures on the upper than on the lower surface so that a net lift force is produced. Note that the square of the velocity is plotted since this quantity is proportional to the pressure; the difference between the upper and lower surface curves is basically the net pressure force.

In the lifting case shown in Fig. 5-2, the upper surface velocity is approximately 26% greater than the free stream velocity. Therefore as the free stream Mach number approaches 0.8, the velocity on the upper surface approaches the sonic value, i.e. M=1. Thus the surface of the airfoil starts to feel compressibility effects before the free stream would suggest they are important. We may define the critical Mach number for an airfoil as that free stream Mach number at which the velocity at some point on the surface of the airfoil reaches the sonic value. For the airfoil considered the critical Mach number Mcrit=0.78 for cl=0 and Mcrit=0.79 for cl=0.22. Ref. 5-2 presents graphs of Mcrit as a

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function of free stream Mach number M for a wide variety of NACA airfoils. We will make use of this material when we estimate drag in Chapter 7. Research into means of delaying the onset of compressibility effects led to the development of the “supercritical” airfoil (Ref. 5-6) by Richard Whitcomb, a NASA researcher who also pioneered the “area rule” that prompted a “coke-bottle” shape for fuselages that reduced transonic drag.

Figure 5-2 Theoretical velocity distribution on upper and lower surfaces of a symmetric airfoil for zero lift and moderate lift angles of attack

Since speed is of importance in air transport modern airliners are designed to cruise as close to sonic speed as is possible without undue drag penalty. Note that though there is continuing interest in supersonic transports, the generation of ground-level pressure disturbances (“sonic booms”) has limited the supersonic portions of flight to those over the sea. As a consequence, supersonic transports are very specialized vehicles and their design is outside the scope of this handbook. As just pointed out, flight at Mach numbers above 0.65 results in regions of supersonic flow developing over the wing. The deceleration of the supersonic flow to subsonic values over the aft sections of the wing produces shock waves which disturb the boundary layer flow there and can cause substantial flow separation with the concomitant penalty of increased drag. A schematic illustration of the flow field and pressure distributions over conventional and supercritical airfoils, as presented in Ref. 5-4, is shown in Fig. 5-3.

The supercritical airfoil has a flatter upper surface designed to provide a smoother deceleration of the supersonic flow so that a weaker shock wave is produced than on the conventional airfoil. The evolution of the shape of the supercritical airfoils is shown in Fig. 5-4.

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(v/V)2

x/c

Figure 5-3 The flow field and pressure distribution over conventional and supercritical airfoils (from Ref. 5-4)

Figure 5-4 Evolution of the shape of typical supercritical airfoils (Ref. 5-4)

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The extent of drag reduction possible is shown in Fig. 5-5 for a 13.5% thick slotted supercritical airfoil, an 11% thick integral supercritical airfoil, and a 12% thick conventional NACA 641-212 low-drag airfoil.

Figure 5-5 Drag coefficient as a function of Mach number for two supercritical airfoils and one conventional airfoil as presented in Ref. 5-4

The slotted supercritical airfoil displays a larger drag coefficient because of the skin friction on the larger wetted surface area caused by incorporating the slot. The major improvement provided by the supercritical airfoil design is found to be in delaying the onset of the drag divergence Mach number from MDD=0.7 for the conventional airfoil to MDD=0.8 for the supercritical airfoils. The drag divergence Mach number is defined as that Mach number where the derivative of the drag coefficient with respect to Mach number has a particular value; NASA uses 10% as its criterion, i.e. dcd/dM=0.10. Thus the use of supercritical airfoils on the wings of modern airliners has provided substantial performance increases. These wing designs are so valuable that aircraft manufacturers consider them proprietary and detailed information on them is not made readily available. As a consequence, for the present purposes of determining the lifting characteristics of the airplane being designed, the NACA airfoils will be considered satisfactory. The issue of the drag reductions possible will be treated in Chapter 7.

There are some additional benefits of the supercritical airfoil in that the lift is preserved and even augmented at the higher free stream Mach numbers possible. This is shown in Fig. 5-6 where the normal force coefficient for the integral supercritical airfoil and the

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NACA 641-212 conventional airfoil is shown as a function of free stream Mach number. However, there is an increase in pitching moment, as shown in Fig. 5-6, that turns out to be not as much of a trim drag penalty for swept-wing aircraft fitted with supercritical airfoils as the optimum wing twist increases as the Mach number increases. This increased wing twist alleviates the penalty arising from increased pitching moment coefficient.

Figure 5-6 The normal force coefficients for a supercritical and a conventional airfoil as a function of free stream Mach numbers, from Ref. 5-4

5.4 Determination of Wing Lift Curve Slope The three-dimensional lift-curve slope of conventional wings CL is given, per radian, by the following equation:

(5-1)

Thus CL is a function of wing aspect ratio, mid-chord sweep angle c/2, Mach number, and airfoil section (defined parallel to the free stream) lift-curve slope. The factor in the figure is the ratio of the actual two-dimensional (i.e., airfoil) lift-curve slope (per radian) at the appropriate Mach number to the theoretical value at that Mach number, [(cl ]/ [Note that the theoretical correction for subsonic compressibility iscl)M cl so in the absence of an experimental value for cl)M the value for= cl/2, that is, the ratio of the actual low-speed airfoil lift-curve slope to that of the airfoil

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in ideal incompressible flow will suffice. The section lift-curve slope (per degree) is obtained from Table 4.1.1-A or Table 4.1.1-B of Appendix C and is the Prandtl-Glauert factor

A sweep-conversion formula, from which the mid-chord sweep for any straight-tapered wing may be determined, is given as follows:

where is the taper ratio, ct/cr. An equation which relates the sweepback angle of the leading edge to any other constant percent chord line (n = %c/100), for trapezoidal wing planforms, is given by

For example, if the quarter chord sweepback angle is known, (n = 1/4 = 0.25) the sweepback angle of the leading edge is easily determined. In a similar fashion, once the sweepback angle of the leading edge is known, the sweepback angle of any other constant percent chord line can be easily found:

5.5 Wing Maximum Lift Section 4.1.3.4 of DATCOM (Ref. 5-1), given in Appendix D, presents methods of rapidly estimating the maximum lift and angle of attack for maximum lift of wings at subsonic, transonic, supersonic, and hypersonic speeds. At subsonic speeds a distinction is made between low and high aspect ratio wings. This is because two different sets of parameters are required to describe the wing characteristics in the two aspect ratio regimes. Specifically, the maximum lift of high aspect ratio wings at subsonic speeds is directly related to the maximum lift of the wing airfoil sections. Wing planform shape does influence the maximum lift obtainable, but its effect is distinctly subordinate to the influence of the section characteristics. For low aspect ratio wings, on the other hand, wing maximum lift is primarily related to planform shape, while the airfoil section characteristics are secondary. For the above reasons, an accurate description of the maximum lift characteristics of wings at subsonic speeds requires the development of separate charts based on different parameters for the high and low aspect ratio regimes. We are concerned with high aspect ratio wings so only the portion of DATCOM pertinent to such wings is presented here.

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5.6 Subsonic Maximum Lift of High-Aspect-Ratio Wings For high-aspect-ratio wings, the three-dimensional maximum lift and stalling characteristics are, to a first approximation, determined by section properties which, for NACA sections are presented in Appendix C (see Section 4.1.1.4 of DATCOM, Ref. 5-1, for methods for dealing with non-standard airfoils). There are, however, certain three-dimensional effects that may become important. These include the spanwise variations of induced camber and angle of attack, respectively, and the effect of spanwise pressure gradient on the boundary layer. Because of these effects, the stall of three-dimensional wings, even untwisted wings of constant airfoil section, usually starts at some spanwise station and rapidly spreads with increasing angle of attack. Highly tapered wings tend to stall at the tips, while untapered wings tend to stall at the root.

On swept wings the induced effects combine to promote stall at the tip. The induced camber at the tip is negative and the induced angle of attack is high. The spanwise pressure gradient tends to draw the boundary layer from the wing root to the tip. All of these factors promote separation at the wing tip and suppress it at the root. It is therefore almost impossible to prevent tip separation at high angles of attack on highly swept wings. Regardless of where the separation first appears, it is the type of separation that determines the maximum lift. Trailing-edge separation, which is characteristic of thick wings, always results in a loss in maximum lift compared to the airfoil-section maximum lift. Leading-edge separation, where the flow rolls up into a spanwise vortex, as on thin swept wings, results in an increase in lift. The magnitude of the increase is related to the strength of the leading-edge vortex. These effects are illustrated by the variations of maximum lift with wing thickness at high sweep angles.

Reynolds number variation has only a slight effect on the maximum lift of wings with very sharp leading edges that separate from the leading edge. Very thick wings are sensitive to Reynolds number in the same way as thick two-dimensional sections. Certain intermediate wings separate from either the leading edge or the trailing edge, depending on the Reynolds number. Caution must be used in extrapolating low Reynolds number data to high Reynolds number in these cases. Slats, flaps, and other devices may be used to modify or control flow separation. Mach number effects on the maximum lift of unswept, thick wings are quite severe, and start at M ~ 0.2. This is to be expected from the analogy with section characteristics. For swept wings the losses due to Mach number are much less than they are for straight wings of a given thickness.

It must be recognized that the maximum lift of the wing alone, as given in this Section, may be substantially altered by interference effects. The addition of fuselages, nacelles, pylons, and other protuberances can markedly change the aerodynamic characteristics of a given configuration near the stall. Interference effects of this type are discussed in Section 4.3.1.4 of DATCOM (Ref. 5-1).

5.7 DATCOM Method for Untwisted, Constant-Section Wings An empirically derived method, based on experimental data, for predicting the subsonic maximum lift and the angle of attack for maximum lift of high-aspect-ratio, untwisted,

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constant-section (symmetrical or cambered) wings is given. The development follows the DATCOM method given in Appendix D. The equations and directions for using the charts are as follows:

The first term on the right side of the first equation is the maximum lift coefficient at M = 0.2, and the second term is the lift increment to be added for Mach numbers between 0.2 and 0.6. Here is obtained from Fig. 4.1.3.4-21a, where is the section maximum lift coefficient at M = 0.2 obtained from Table 4.1.1-A, and is a Mach number correction obtained from Fig. 4.1.3.4-22. In the second of the two equations is the wing lift-curve slope, for the Mach number under consideration, obtained previously from Eq. (5-1), is the wing zero-lift angle of attack (same as the airfoil zero-lift angle of attack), again for the Mach number under consideration, obtained from Table 4.1.1-A or Table 4.1.1-B, and is valid for all Mach numbers up to 0.6 and is obtained from Fig. 4.1.3.4-21b. For cruise Mach numbers greater than 0.6, no general empirical correlation is readily available, so the low speed value is used. For preliminary design purposes this increment is not of great importance since flight under normal conditions will not involve maximum lift at the cruise speed.

The leading-edge parameter y, which does not explicitly appear in the equations, must be used in reading values from the charts. The value of y is expressed in percent chord and is obtained or approximated with the aid of Fig.2.2.1-8 in Appendix A. In calculating the value of CLmax calculated from Equation 1 is used as the numerator of the first term of Equation 2. Sample problems are carried out in Appendix D; the appropriate one to consider is sample problem 1 which uses Method 2 for subsonic speeds.

5.8 DATCOM Method for Twisted Wings with Varying Airfoil Sections High-aspect-ratio wings are often twisted along a spanwise axis and have varying airfoil sections, in order to obtain favorable stalling characteristics. A span-load approach that is generally used gives reasonable results for unswept, high-aspect-ratio wings. The method does not, however, give good results for swept wings because of the strong spanwise flow on swept wings. The method is given in some detail in Appendix D and proceeds as follows (referring to sketch a in Appendix D):

1. Plot the section lift coefficient for the given wing as a function of spanwise station for the appropriate Reynolds number and Mach number.

2. Using any appropriate theoretical wing-span-loading method, plot the lift coefficient as a function of span position and angle of attack.

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3. The angle of attack and spanwise position for initial stall is determined by the angle of attack at which the curves of steps 1 and 2 become tangent.

The integrated value of the curve of Step 2 approximates the maximum lift coefficient of the wing. For high-aspect-ratio swept wings with twist, it is suggested that maximum-lift values be estimated by comparison with tests of similar configurations from the literature.

5.9 Determination of Wing Maximum Lift in the Cruise Configuration The DATCOM approach has been described in Section 5.7 from which we find

This relation is applicable provided that:

where C1 is obtained from Fig. 4.1.3.4-24 of Appendix D. This equation applies to untwisted constant section wings which is not strictly applicable because the wings designed should have anywhere between 3 to 5 degrees of washout, and even greater amounts if a highly tapered straight wing is used. For example, the Lockheed Viking SA-3 has a straight wing, a taper ratio of 0.3, and uses 11o of washout. Turboprop or turbofan transport aircraft generally use wings that are considered to be of high aspect ratio and will meet the condition required of the equation. Review the market survey for reasonable values of wing aspect ratio.

Recall that the ratio is obtained from Fig. 4.1.3.4-21a while the value of clmax

has been determined previously. The Mach number correction to CLmax, namely CLmax , is obtained from Fig. 4.1.3.4-22 as a function of Mach number, y , and leading edge sweepback angle. A plot of CLmax vs Mach number in the range 0.2<M<0.6 should be made and used in the determination of minimum flying speed in the performance section of the report.

5.10 Determination Of CL,max For The Take-Off And Landing Configurations It is suggested that reasonable values of the T. E. (trailing edge) and L. E. (leading edge) flap layouts be chosen based on the market survey aircraft and for deflections the guidelines given below should be considered:

Condition Typical Flap Deflection (in degrees)

Take off 15<TE<25; LE<20 Landing 40<TE<50 or 60; LE<20

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The procedure for estimating the increment of CLmax for the wing with flaps deflected is given in DATCOM Section 6.1.4.3. In order to use the results given there it is first necessary to estimate the airfoil section value of clmax due to flap deflection. Section 6.1.1.3 of DATCOM, which appears in Appendix E, is used for this. The material (graphs, equations) necessary to carry out these calculations are contained herein. A curve of section lift coefficient versus angle of attack is given in Sketch (a) of Appendix E. The sketch shows the relevant sections of DATCOM used in producing the curve. A good description of high lift devices and control surfaces and their placement on the wings is given in Torenbeek (Ref. 5-6, pp. 252-262). An illustration of the general effect of different high-lift devices on the section maximum lift coefficient is shown in Fig. 5-7. Each of these devices has different drag penalties associated with their operation and this will be addressed in Chapter 7.

Note that the value of clmax for the chosen design is known from the work done previously, namely the airfoil selection process. It is seen that clmax with flaps deflected is given simply as the sum (clmax)flap=0 + clmax, flap

Figure 5-7 The general effect of various high-lift devices and combinations on the airfoil section maximum lift coefficient cl,max

5.11 Airfoil with Trailing-Edge Flaps An empirical method for predicting airfoil maximum lift increments for plain, split, and slotted flaps is presented in Figs. 6.1.1.3-12 and 6.1.1.3-13. The maximum lift increment

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cl,max

is given by

where (clmax)base is the section maximum lift increment for 25 percent-chord flaps at the reference flap-deflection angle from Fig. 6.1.1.3-12a, k1 is a factor accounting for flap-chord-to-airfoil-chord ratios other than 0.25 from Fig. 6.1.1.3-12b, k2 is a factor accounting for flap deflections other than the reference values from Fig. 6.1.1.3-13a, and k3 is a factor accounting for flap motion as a function of flap deflection from Fig. 6.1.1.3-13b. Sample problems are given in Appendix E.

5.12 Airfoil with Leading-Edge Slats or FlapsA method has been developed for predicting the stall of thin airfoils with leading-edge flaps or slats. Modern airliners generally are equipped with slats since they are relatively simple and provide lift augmentation with little drag penalty. When leading edge flaps are used they are generally Krueger flaps (see Torenbeek, Ref. 5-7), and the approach presented is not applicable to them. The estimation method, which is presented in Appendix E, is based on the assumption that the flapped and unflapped airfoils stall when the respective pressure distribution about the noses are the same. This method is carried out with the aid of Figs. 6.1.1.3-14, -15, and -16 in Appendix E. It should not be used for slat deflections greater than 20o or slat-chord-to-airfoil-chord ratios greater than 0.20. Sample problems are given in Appendix E.

5.13 Determination of Cl,Max for the Wing The increment in maximum lift coefficient for the wing due to the trailing edge flap deflection is given in Section 6.1.4.3 of DATCOM, Ref. 5-1, by the following equation:

where cl,max is obtained as described previously. The quantity SWf /S is the ratio of wing area affected by the trailing edge flap deflection (including both port and starboard wings) to the total wing area as shown in the sketch in Appendix B (from DATCOM page 2.2.2-2), and the quantity = ct /cr is the taper ratio, i.e., the ratio of the tip chord to the root chord. The other quantities are given as follows:

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It should be noted that the flap deflection angles and all dimensions are measured in planes parallel or perpendicular to the plane of symmetry.

The increment in maximum lift coefficient due to leading edge slat deflection, based on the wing reference area is given by

In this equation cf /c is the ratio of the leading edge slat chord to the wing chord, bslat /be is the ratio of the total slat span to the exposed wing span. For a segmented leading edge slat bslat is the sum of all the segment spans, and c/4 is the sweep angle of the quarter-chord line.

Two values of the total CL,max should be calculated; one for take off and the other for landing.

5.14 Sample Calculation A sample problem for the trailing edge flap is given for a wing-flap configuration described as follows:

A = 5.1 = 0.383 c/4 = 46o

NACA 64210 airfoil t/c = 0.72 (streamwise)Single-slotted flap cf /c = 0.258 f = 15.6o

Sf /S = 0.378 Re,l = 6.0 x 106

Compute (figure and equation numbers refer to DATCOM results found in Appendix E)

(cl,max)base= 1.045 (Fig. 6.1.1.3-12a)k1 = 1.010 (Fig. 6.1.1.3-12b)

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k2 = 0.605 (Fig. 6.1.1.3-13a)(flap angle)/(reference flap angle) = 15.6/45

=0.347k3 = 0.445 (Fig.6.1.1.3-13b) (cl,max) = k1k2k3(cl,max)base

= (1.010)(0.605)(0.445)(1.045) = 0.284 (Eq. 6.1.1.3-a)

K = 0.730Solution:

CL,max = cl,max(Sf /S)K = (0.284) (0.378) (0.730) = 0.0784 (based on S)

This compares with a test value of 0.075.

5.15 Presentation of Maximum Lift Coefficient Results The format in Table 5-1 is suggested for presenting the results of the study to determine the maximum lift coefficients. Note that the numerical values shown in the sample table are merely representative of a typical design. There should also be presented a planform view of the wing showing the location of flaps and other control devices (for example, see Fig. 7-27 in Torenbeek, Ref. 5-7)

Table 5-1 Summary of Estimated Values of CL,max

Airfoil Choice : NACA 64,-212 (ROOT)NACA 64,-209 (TIP)

Aspect Ratio : A = 6.25Taper Ratio : = .333Flap Type (cf /c) : Fowler, (23%)Spanwise Extent (i and o) : 16.4% and 76.0%Rated Area (SWf /S) : 0.53

Configuration flap, trailing edge

in degreesflap ,leading

in degreesCL,max low speed M=0.2

CL,max

cruise speedM=0.8

Cruise 0 0 1.23 0.99Take-off 25 0 1.64 -Landing 40 20 1.92 -

5.16 Tailplane Design The vertical and horizontal tails are primarily stability and control appendages and a simplified approach for sizing the horizontal tail is given in Appendix K. This method is provided for reference purposes and need not be treated in the design report. Instead, the market survey aircraft will be used as a guide for the choice of the tail configuration. It is important to determine the following tail surface characteristics from the market survey information:

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Sv - the area of the vertical taillv - the distance from the aerodynamic center of the vertical tail

to the center of gravity of the aircraft (see p. 294 in Torenbeek)

Sh - the area of the horizontal taillh - the distance from the aerodynamic center of the horizontal

tail to the center of gravity of the aircraft

These properties are used to form the characteristic parameters for the tail surfaces: the volume coefficient of the vertical tail

and the volume coefficient of the horizontal tail

where S is the wing area and is the mean aerodynamic chord (MAC) of the wing. Discussion of these ratios along with representative values may be found in Torenbeek (Ref. 5-5, pp. 326-339). The tail surface areas are obtained by considering the reasonable extrapolation of the leading and trailing edges in to the fuselage centerline, as is done for the wing. Tail areas are typically in the range of 0.2 < Sh/S < 0.35 and 0.15 < Sv/S <0.25.

The horizontal and vertical tail surfaces are generally highly swept in order to make their effective moment arms as long as possible, while also helping to maintain their critical Mach numbers higher than that of the wing. The airfoils for the tail surfaces are generally symmetrical sections so as to produce the same force magnitude for a given deflection angle. At the same time, the airfoils for the tail surfaces have thickness ratios smaller than that of the wing to also help keep the critical Mach number of the tail surfaces higher than that of the wing. The thinner sections are practical because they save weight and are possible because of the smaller aerodynamic loads they experience. The aerodynamic center for a tail surface may be taken as the 1/4 chord point of the mean aerodynamic chord of the surface in question. The center of gravity position of the market survey aircraft may be approximately located at the 1/5 chord point of the MAC of the wing.

A tabular presentation of the data for the market survey aircraft should include aircraft designation, take-off weight, wing area, MAC of the wing, tail areas, length of the fuselage, the lengths lv and lh, the MAC of the vertical and horizontal tails, and the vertical and horizontal volume coefficients. The results should be examined for trends in the variation of Vv and Vh, (for example, how do they vary with take-off weight?), and values should be selected for the design aircraft taking any of these variations into account. Having values for Vv, Vh, S, , and fuselage length for the design aircraft it is then possible to first find Svlv and Shlh. The values for lv and lh for the market survey

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together with the associated fuselage length should permit an estimate for lv and lh for the design aircraft to be made. Finally the areas Sv and Sh for the design aircraft may be determined. The sweepback angle, aspect ratio, taper ratio, and airfoil section may be chosen by using the market survey results as a guide.

The airplane has how been sized completely and once the wing location is determined by the methods presented in Chapter 6, a full three-view CAD diagram can be generated to illustrate the overall design.

5.17 Wingtip TreatmentsAs described in the discussion of flow over finite wings in Appendix L, the trailing vortex sheet induces a swirling component into the flow field in the vicinity of the wing. At the same time it was demonstrated that the distribution of lift across the span influences the induced drag arising as a result of the trailing vortex sheet. The downwash at the lifting line tilts the velocity vector down by an amount equal to the induced angle of attack, tan-1(w/V). This then tilts the lift vector away from the normal to the free stream velocity producing a force component in the drag direction, and that component is the induced drag. Increasing the aspect ratio factor of the wing reduces the induced drag since the induced drag coefficient is

The aspect ratio is A=b2/S so the induced drag is proportional to the square of the span loading

Although this effect is beneficial it has drawbacks; increasing the span for the same lift effectively makes the wing more slender in planform leading to increased bending moment at the root of the wing. The increased bending moment must be countered by a strengthened structure which typically involves additional weight. By the same token, increased span can be a limiting factor in ground operations of commercial aircraft. Thus, the desire to improve the efficiency of aircraft by reducing wing drag has inherent limitations that must be considered.

The current rapid rise in fuel costs has made the search for drag reduction techniques even more important. Because induced drag is a large fraction of the total drag for subsonic aircraft, on the order of 50%, modifications of the spanwise lift distributions which reduce induced drag are desirable. Two wing tip treatments have received substantial attention from airplane manufacturers and operators: winglets and raked wing tips. These two types of wing tips are shown schematically in Fig. 5-8. The winglet case

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presents a non-planar wing because the tips of the wing are not in the plane of the major portion of the wing. The raked wing tip presents a case of leading and trailing edges which are not straight although the wing remains planar.

Figure 5-8 Two popular wing tip treatments: (a) winglet and (b) raked tip

5.17.1 Winglets The flow around the tips of a finite wing involves a whirling motion caused by the difference in pressure between the upper and lower surfaces of the wing, as illustrated schematically in Fig. 5- 9. Therefore there is an inboard flow on the upper surface and an outboard flow on the lower surface. The swirling flow downstream of the trailing edge of the wing organizes, that is, “rolls up” itself into two concentrated trailing vortices after a distance on the order of the wingspan. It seems clear that preventing this motion would increase the total lift produced and a simple solution would appear to be the placement of endplates at each wing tip to block the cross-flow. This solution however mainly introduces increased drag due to the increased surface area thereby any benefit it might appear to have in improving lift. A more sophisticated exploitation of the three-dimensional flow field itself can indeed reduce the induced drag produced by the wing downwash.

In much the same way that a sailboat may be sailed against the wind by appropriate pointing of the sail, the placement of a winglet in such a fashion as to actually produce a negative drag force, that is, a thrust would be a distinct advantage. A view of the flow looking down on the upper surface of the wing with a winglet mounted vertically on the tip is shown in Fig. 5-10.

(a) winglet (b) Raked tip

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Figure 5-9 Schematic illustration of the flow over a finite lifting wing: (a) a front view looking at the leading edge and showing the cross-flow velocity components produced by the higher pressures on the bottom wing surface and lower pressures on the top wing surface; (b) a top view looking down on the wing illustrating the velocity on the top surface (solid arrows) and on the bottom surface (dashed arrows).

The resultant force in the flight direction produced by the three-dimensional flow on the winglet is given by

This force is a thrust force so that the drag of the wing is reduced. The actual design of the winglet is rather complicated and tends to have superior performance only in the vicinity of the design point chosen, for example, the cruise condition. Discussion of winglets may be found in current textbooks on aerodynamics, for example Refs. 5-5 and 5-7. Early research on winglets applied to subsonic jet transports is reported in Ref. 5-8 and current research is described in Ref. 5-9. An interesting general discussion of the subject is presented by Jones in Ref. 5-10.

Vortex roll-up region

Trailing vortex

V

Trailing vortex

Inboard flow on top of wing

Outboard flow on bottom of wing(a)

(b)

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Figure 5-10 View looking down on the upper surface of the port wing showing the resultant velocity VR producing a resultant force R on the vertically

mounted winglet, here represented as a simple flat plate. The magnitude of the angle is exaggerated for clarity

The important design variables for the winglet are

the leading edge sweep angle of the winglet the cant angle measured between the vertical and the plane of the winglet the toe-in angle measured between the flight direction and the winglet root

The winglet doesn’t add the additional wing root bending moment that would be developed if the span was merely increased by the height of the winglet which is a benefit. On the other hand, there are local forces and moments at the winglet junction with the wing and these tend to add some weight to the wing. Note that the action of the winglet is tied to properly exploiting the induced whirling flow generated by the finite wing so a winglet may be employed above the wing, below the wing, or both. The performance of a winglet is difficult to generalize in the preliminary design process and consideration of winglets is typically left to later detail design stages. As a consequence winglets will not be part of the design procedures carried out here, although in recognition of their fairly widespread use they may be employed on configuration concept drawings, using market survey information as a guide.

5.17.2 Raked Wing Tips Boeing has been prominent in the application of raked wing tips to their latest aircraft rather than winglets. The efforts at modifying the wing tips are aimed at altering the spanwise loading in order to achieve reduced induced drag. The idea may be broadly understood as taking a wing of given span and then increasing

R

L

D

V

W

VR

winglet

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the span to achieve the corresponding reduction in the induced drag coefficient. This extended wing tip may be bent up to fashion a winglet or swept back further to form a raked wing tip. The details of the flow resulting from such changes are important to determining whether worthwhile improvements can be achieved. Of course, in addition to any performance improvements which may accrue to the wing tip treatment the other effects such as structural loading, weight implications, off-design performance, and the like must be assessed. A detailed computational and experimental study of raked wing tips is presented in Ref. 5-11. It is pointed out there that the trailing vortex sheet behind a swept wing deforms rapidly and is not well described by classical wing theory as described in Appendix L. Nonlinear effects and non-planar attributes of the trailing vortex sheet must be treated by more sophisticated lifting surface methods. The performance improvements accruing to raked wing tips, or to winglets, are difficult to quantify in a general manner. Therefore, as in the case of winglets, such wing tip treatments must be deferred to later stage detailed design evaluations

5.17 References

5-1. Hoak, D.E., et al: "USAF Stability and Control DATCOM", Flight Control Division, Air Force Flight Dynamics Laboratory, Wright-Patterson AFB, April1978.

5-2. Abbott, I.H., et al: "Summary of Airfoil Data", NACA Technical Report No. 824, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930090976_1993090976.pdf

5-3. Abbott, I.H. and Von Doenhoff, A.E.: Theory of Wing Sections, Dover, NY, 1959.

5-4 Harris, C.D.: “NASA Supercritical Airfoils”, NASA Technical Paper 2969, March, 1990. See also: http://hdl.handle.net/2002/13874

5-5. McCormick, B.H: Aerodynamics, Aeronautics, and Flight Mechanics, Wiley, NY 1995.

5-6 Whitcomb, R.T. and Clark, L.R.: “An Airfoil Shape for Efficient Flight at Supercritical Mach Numbers”, NASA TM X-1109, 1965

5-7. Torenbeek, E.: Synthesis of Subsonic Airplane Design, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1982.

5-8 Bertin J.J. and Smith L.M.: Aerodynamics for Engineers, Third Edition, Prentice-Hall, New Jersey, 1998

5-9 Flechner, S.G., Jacobs, P.F., and Whitcomb, R.T.: “A High Subsonic Speed Wind Tunnel Investigation of Winglets on a Representative Second Generation Jet Transport Wing,” NASA Technical Note TN-8264, July 1976

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5-10 Lazos, B.S. and Visser, K.D.: “Aerodynamic Comparison of Hyper-Elliptic Cambered Span (HECS) Wings with Conventional Configurations,” AIAA 2006-3469, 25th AIAA Applied Aerodynamics Conference, San Francisco, 2006

5-11 Jones, R.T.: “Minimizing Induced Drag”, Soaring, October 1979, pp.26-29.

5-12 Vijgen, P.M.H.W., Van Dam, C.P., and Holmes, B.: “Sheared Wing-Tip Aerodynamics”, Journal of Aircraft, Vol. 26, No. 3, March 1989, pp. 207-213

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