• Section 10.2 presents helpful design information for the selection of leading edge high-lift systems.

• Section 10.3 presents helpful design information for the selection of trailing edge high-lift systems or flaps.

• Section 10.4 presents methods to estimate the impact of adding partial span high-lift devices.

• Section 10.5 introduces a number of different wingtip options and discusses their advantages and disadvantages.

General Design Guidelines

NACA TN-3007 [1] provides helpful guidelines for the initial design of a fixed slot. Using a symmetrical NACA 64A010 airfoil, the results of an investigation of combinations of a leading edge slat and flap, and split flap and a double-slotted flap are presented. With respect to the leading edge flap, the investigation showed that for R_e ≈ 2 × 10⁶ a droop deflection δ_s = 40° resulted in the highest C_lmax. For higher R_e, δ_s = 30° was found to result in the highest C_lmax. The reference did not investigate drag.

Aerodynamic Properties

Results for the hinged leading edge using a NACA 64A010 airfoil are given in Table 10-1 and are obtained from Ref. [1], for a Reynolds number of 6 × 10⁶. Results for other airfoils and conditions are likely to be different. A maximum change in maximum section lift coefficient to be expected is ΔC_lmax ≈ 0.56. This will increase the stall AOA by about Δα_max ≈ 7.8°, and the change in pitching moment coefficient is approximately ΔC_m ≈ -0.048.

As intuition would hold, the maximum lift coefficient increases with the deflection of the hinged leading edge, up to a maximum around 30°. The variation of C_lmax is plotted against the deflection in Figure 10-4. Higher deflections reduce this maximum and can be attributed to separation of effects caused by the sharp curvature around the hingeline.

Summary

Aerodynamic Properties

Not available at this time. In the absence of better data, aerodynamic properties are expected to be similar to those of the droop nose leading edge flap, which are presented in Table 10-1.

General Design Guidelines

NACA TR-407 [6] provides helpful guidelines for the initial design of a fixed slot. Spurred by the popularity of the Handley-Page slat, which would increase drag by a factor of more than 3 when deployed, the report details the investigation of a series of fixed slots in an attempt to reduce the minimum drag coefficient without detrimentally affecting the maximum lift coefficient and the stall AOA of a Clark Y airfoil. Of the configurations tested, the one shown in Figure 10-8 was found to yield the best results. It was found that reducing the drag coefficient of the auxiliary airfoil does not necessarily reduce the drag of the combination and may even cause it to increase and the maximum lift to decrease. Rounding the nose of the main airfoil was determined to be the most promising way to reduce the drag of the combination. It was also shown that moving the depth of the slot aft (to the right in Figure 10-8) did not have appreciable effect on the aerodynamic characteristics of the combination.

Aerodynamic Properties

Results for the fixed slot using a Clark Y airfoil are given in Figure 10-9 and Table 10-1 and are obtained from Ref. [6]. The test Reynolds number was about 0.63 × 10⁶. A maximum change in maximum section lift coefficient to be expected is ΔC_lmax ≈ 0.45, about 0.11 less than that of the hinged leading edge. This will increase the stall AOA by about Δα_max ≈ 9°, the zero AOA lift coefficient will drop by about ΔC_lo ≈ −0.074, and the minimum drag coefficient will increase by about ΔC_dmin ≈ 0.0079 (79 drag counts). Ultimately, the gain depends on the shape and the experimental setup does not represent an optimized geometry.

Summary

Simple Krüger Flap

The simple Krüger flap is a high-lift device intended to increase the curvature of the camber of the airfoil to which it is mounted. It is used in some commercial jetliners to improve the high-lift capability of the under-cambered airfoil near the root of the fuselage² and delay flow separation. As such, it is primarily used on the inboard part of the wing. The outside mold line (OML) of the device is essentially shaped like the lower surface of the leading edge of the airfoil. Its geometry is highly dependent on the geometry of the leading edge and this inflicts an aerodynamic limitation on its shape. The effectiveness of the simple Krüger flap with variations in AOA is generally considered poor. It is not used on any modern airplane. The flap rotates into a position that is approximately 110° to 140° with respect to the chord line (see Figure 10-10). Examples of aircraft that use the simple Krüger flap are (as previously mentioned) the Boeing 707, Convair 880, and Convair 990, which featured it from root to tip.

Design Guidelines

The function of the Krüger flap is explained by noting that at the proper deflection angle the stagnation point of the incoming airflow is positioned near the leading edge of the flap. This reduces the excessive airspeed over the leading edge of the airfoil by allowing the airflow to accelerate over a longer distance. The reduction in local airspeeds, in turn, means the associated pressure peaks are reduced and this delays the formation of flow separation (see schematic in Figure 10-11). Consequently, the airfoil stalls at a higher AOA [7, pp. 170–171]. In short, the general design requires a trial and error approach through extensive wind tunnel testing, although some basic design guidelines can be presented.

Krüger investigated the device in NACA TM-1177 [9], with and without the presence of a split flap. He found that the chord length of the flap, C_S, should be 0.07C to 0.10C, where C is the airfoil chord length. He tested two chord lengths, one which was 0.05C and the other 0.10C, and found the shorter one actually reduced the maximum lift. From this he concluded that a minimum chord length should be 0.07C, as shown in Figure 10-10. He suggested the leading edge of the flap should feature a ball at the leading edge with a radius around 0.167 C_S, although increasing it to 0.334 C_S showed no detriment. However, allowing air to flow through a gap between the flap and the leading edge of the wing reduced the increase in ΔC_lmax, cited below, by about 50%–70%.

Aerodynamic Properties

Results for a 0.01·C Krüger flap using a Mustang 2 airfoil are given in Table 10-1. The test Reynolds number was about 2.14 × 10⁶. Per Ref. [9] the maximum increase in ΔC_lmax for the Krüger alone without trailing edge flaps amounted to ΔC_lmax ≈ 0.30, at a deflection angle δ_s = 130°. In fact, it must swing through approximately 90° before it even begins to increase the C_lmax. This gain is negatively affected by the presence of a deflected trailing edge flap. The reference also tested a 0.2·C split flap at 60° deflection and found that with the flap ΔC_lmax increased only by 0.15, albeit for δ_s ranging from 100° to 120°. It is also stated that there was a substantial reduction in the magnitude of the low pressure region on the leading edge.

The Krüger flap will increase the stall AOA by about Δα_max ≈ 5°, zero AOA lift coefficient will drop by about ΔC_lo ≈ −0.093, and the minimum drag coefficient will increase by about ΔC_dmin ≈ 0.0149 (149 drag counts), so it add substantial drag to the airplane. Change in pitching moment coefficient is approximately ΔC_m ≈ −0.027. The combination of the Krüger flap and the 0.2·C split flap increased the stall AOA by some Δα_max ≈ 0.7°. While this may not seem like much, the reader is reminded that the primary purpose of the high-lift devices is to increase the lift without changing the stall AOA excessively (i.e. making it too large or too small).

Summary

Folding, Bull-nose Krüger Flap

The folding, bull-nose Krüger flap is an improvement over the simple Krüger flap, as it increases the curvature of the airfoil camber. The round bull-nose (see Figure 10-12) improves the effectiveness of the flap over a larger range of AOA by providing a larger area in which to “capture” the stagnation point. Just like the simple Krüger flap, the flap is a two-position device (retracted-deployed) whose deployed position is generally biased toward landing (C_Lmax) and not T-O. The folding, bull-nose Krüger flap is clearly more complicated than the simple one and often requires a slaved mechanical linkage that folds the bull-nose into the deployed and retracted positions. The flap is used on the Boeing 727 (see Figure 10-1 and Figure 10-12), 737, and 747 (see Figure 10-14) jetliners.

As with the simple Krüger flap, the drawback is a limited increase in C_Lmax. As with the simple Krüger flap, the rigid flap is highly dependent on the lower surface of the leading edge and this may inflict an aerodynamic detriment to the geometry. However, it can be the ideal surface to control stall progression along the wing.

Aerodynamic Properties

In the absence of design data assume the properties discussed above for the simple Krüger flap. Results for the simple Krüger flap are given in Table 10-1.

Variable-camber Krüger Flap

The variable-camber Krüger flap is intended to improve the shape of the simple and bull-nose Krügers. It is capable of developing far superior curvature, greatly improving its aerodynamic properties when compared to the others. It is a two-position device (retracted-deployed). The deployed position is generally biased toward landing (C_Lmax) and not T-O. Each flap panel must be flexible and is thus usually made from fiberglass and in short sections (spanwise speaking). Two hat sections parallel to the leading edge are used to stiffen it in the spanwise direction and ensure chordwise flex only.

The flap deflects through approximately 120° angle from the stowed position (depending on leading edge geometry), during which it transforms from a more or less flat panel into a highly curved one. This feat requires a complex four-bar linkage to make certain it acquires the right shape and position (see schematic in Figure 10-13). This mechanism also explains why the device is so far only a two-position one. Adding a third position (say a T-O setting) that does not violate the quality of the other positions is destined to be challenging. The flexible panels act like bug shields and protect the leading edge from contamination. Figure 10-14 shows the combination of a bull-nose and variable-camber Krüger flaps on a Boeing 747-400 commercial jetliner.

The sophistication of the actuation mechanism of the flap system is impressive – it is truly a marvel of engineering. However, in order to make the system work reliably, each part has to be made with tight tolerances. As a consequence, it is expensive to manufacture and maintain. The flap must be carefully rigged to prevent undesirable distortion of the panels under high air loads and be preloaded to avoid panel bulging (and the associated drag increase) when retracted.

In spite of the limitations, Krüger flaps should not be ignored as a potential candidate configuration for aircraft designed to sustain a laminar boundary layer over the wing’s upper surface. Since the flap is stowed on the lower surface of the airfoil, an opportunity exists for a smooth upper surface. To the author’s best knowledge, the Boeing 747 is the only aircraft currently in production to use the variable-camber Krüger flap. It was also featured on the proof-of-concept Boeing YC-14, a participant in the USAF Advanced Medium STOL Transport (AMST) project in the late 1970s.

Aerodynamic Properties

In the absence of design data assume the properties discussed above for the simple Krüger flap, although it is undoubtedly much better. Results for the simple Krüger flap are given in Table 10-1.

(1) Extension forward of the leading edge (Δx or a).

(2) Downward drop below the leading edge (Δy or b).

(3) Size of the gap at the outlet of the slot (c).

(4) The rotation of the element (δ_S).

The Airload-actuated Slat (or the Automated Handley-Page Slat)

As stated earlier, the airload-actuated slat is the automated version of Handley-Page's fixed slot. It is arguably an ingenious device designed to be extracted and retracted by the magnitude of the pressure acting at the leading edge of the wing (see Figure 10-17). This way its operation is passive; when the airplane is at a low speed it is automatically deployed and when at high speed the slat is stowed, again automatically. This happens solely due to the action of pressure forces, although some designs feature a spring to help retract the slat. As the airplane must operate at higher AOAs at low speeds, a low-pressure region forms around the leading edge that pulls the element forward out of its stowed position. By the same token, when the airplane’s airspeed increases, its AOA reduces. The stagnation pressure now impinges on the element and forces it back into the stowed position. This system of passive leading edge slats is employed on aircraft like the Messerschmitt Me-262 Schwalbe, SOCATA Rallye 100 and McDonnell Douglas A-4 Skyhawk (see Figure 10-18).

The slat travels in or out from the leading edge, but the actuation rods may be slightly curved, leading to the slat deploying out and rotating through a slight angle downward. In the deployed position, the device increases the pressure drop around the leading edge, increasing the stall AOA and C_Lmax of the wing. The fact that the slat retracts when the airplane accelerates to higher airspeeds reduces its drag significantly compared to the fixed slot. This renders it ideal for aircraft intended for STOL operations, but for which higher cruising speed is also important. Airplanes rolling rapidly at high speeds (fighter aircraft) have been known to occasionally have the slat on the down-travelling wing forced out, while the one on the up-travelling wing remains retracted. The resulting asymmetry may produce a violent roll departure.

The Maxwell Leading Edge Slot

The Maxwell slot is best described as an in-between the fixed slot and slat. Rather than translating and rotating like the standard (or Handley Page) slat, the device operates through rotation only about the leading edge, as is shown in Figure 10-19. From that perspective, the slat is mechanically simple, although the addition of the hinged door adds complexity. However, the cruise configuration of the airfoil is relatively smooth, although it would almost certainly trip the laminar boundary layer on both the upper and lower surfaces if used with an NLF airfoil. The position of the slat is referred to in terms of the gap opening (e.g. 0.01C or 0.0175C, etc.) rather than rotation in degrees, as this will vary based on the airfoil geometry.

The Maxwell slot can also be used without the hinged door shown in Figure 10-19. This will make its installation mechanically simpler and at first glance it will appear more like a fixed slot, however, with one important difference – in cruise, the gap size is zero, whereas it remains constant for the fixed slot. The device is investigated in Refs [11,12]. Reference [11] concludes that the increase in C_lmax of a Maxwell slot is similar to that achievable with a Handley Page slat. Reference [12] found the optimum gap width to be 0.0175·C. The investigation shows that the drag of the slat increases with gap size.

Three-position Slats

The three-position slat is a version of the leading edge slat that features three positions (see Figure 10-20): retracted, take-off, and landing. In the take-off position, the slat either rests against the leading edge of the main airfoil, preventing air from flowing from the lower to the upper surface, or a very narrow slot opens. In this configuration, it works more to increase the camber of the basic airfoil, as the closed slot does not permit circulation to develop around the slat. The ideal motion of the slat is one of forward and downward motion, with limited rotation. The resulting airfoil geometry offers higher L/D than the open slot configuration and this improves T-O and climb performance. In the landing position, the slat rotates to open a slot, offering the maximum improvement in C_Lmax.

The track and mechanism required to move the slat in the above fashion is more complicated than shown in Figure 10-20, as such a system is biased toward translation at first and rotation later. However, many modern aircraft simply feature a circular arc design and live with a narrow slot for the T-O setting. Other aircraft, such as the B-777, have the main airfoil leading edge shaped such that it forms a seal with the trailing edge of the slat. Figure 10-21 shows the three-position slat in action on the MD-80 jetliner. The difference in slot sizes between the second and third setting is clearly visible in the center and right pictures, respectively. The three-position slat is the most common leading edge high-lift device in use today. Practically all commercial jetliners, except the B-747, use the device.

General Design Guidelines

Besides the geometry as noted, the effectiveness of the slat depends on its position and deflection as defined in Figure 10-16. The key design parameters include the chord length, C_S, gap, slot width, a (which is equal to the forward translation, Δx), vertical translation, Δy, and deflection angle, δ_S.

Generally, the chord length should be of the order of 0.15 to 0.175C and the gap around 0.001-0.002·C. The optimum deflection is usually in the neighborhood of 25°. Figure 10-22 shows how the slat deflection angle affects the increase in C_lmax. It is actually a combination of the deflection angle and the gap opening that yields the highest increase.

Note that there is a discrepancy in the literature as to how the chord length is defined. The two options can be seen in Figure 10-15 and Figure 10-19. The interested reader should refer to the cited sources to determine which applies to the published data.

Aerodynamic Properties

Results for slats and Maxwell slots using a NACA 64A010 and Clark Y airfoils are given in Table 10-1. They are obtained from Refs [1,11]. Slats yield a maximum change in maximum section lift coefficient as high as ΔC_lmax ≈ 0.84 for an optimized configuration. For preliminary design, numbers ranging from 0.5 to 0.7 can be used. The slats increase the stall AOA by about Δα_max ≈ 11° while the zero AOA lift coefficient drops by about ΔC_lo ≈ -0.21. This ignores the shift of the lift and assumes the slat will only extend the lift curve upward as shown in Figure 8-58. The minimum drag coefficient increases by about ΔC_dmin ≈ 0.008 (80 drag counts).

Summary for Slats

Summary for Maxwell Flap

How to Use the Tables

Remember that the tables are intended to get you “in the ballpark” during the conceptual design phase. Begin by locating the part of the table containing the type of leading edge flap. Make note of the airfoil and Reynolds number used during the wind tunnel testing, as well as the flap chord and deflection. These are important values to keep in mind if the geometry and operational conditions of the target flap deviate significantly from these values. For values relatively close, it is acceptable to prorate the characteristics of interests (see Example 10-1). The values to be extracted are ΔC_lmax, Δα_max, ΔC_dmin, and ΔC_m.

General Design Guidelines

The primary design variables for the plain flap are flap chord, flap deflection, hingeline location, and flap airfoil. The maximum lift of the plain flap is dependent on the flap chord, which should be of the order of 20%–30%. Some airplanes feature plain flaps for rudders with flap chords as much as 50%. The flap should be oversized by approximately 0.0003·C to 0.0030·C. Thus, if the chord is 3.28 ft (1.00 m), the over-sizing should amount to approximately 0.012′′ to 0.120′′ (0.3–3.0 mm) per side (see Figure 10-25). The purpose of the over-sizing is to re-energize the boundary layer by placing a small obstruction in its way. This helps air stay attached farther aft, improving the effectiveness of the surface at low deflections by preventing it from operating in dead air.

The overhang (see Figure 10-26) plays an important role in reducing hinge moments of the flap, which is imperative if it is to be used as a manually actuated control surface (aileron, elevator, or rudder). However, this may introduce unexpected aerodynamic complexities. Let’s first consider the upper image in the figure. It shows the flap with an overhang that equals the leading edge radius of the flap. In other words, the hingeline is precisely the center of the leading edge arc. This allows the overlapping skin (or trailing edge lip as it is commonly called) to be extended so it practically touches the skin of the flap. Of course, the overlapping skin should never be in direct contact with the flap, as it flexes in flight, which can potentially lead to jamming. For many applications, the small gap may range from 0.050′′ to 0.125′′ (1.3 to 3.2 mm). A careful design of this detail will include an estimation of the most adverse structural deformation of the flap and size the gap to accommodate it. At any rate, the presence of the lip is an important advantage as this prevents a jet of air from the lower surface of the airfoil from streaming through the slot and detrimentally affecting the flow on the upper surface. Its absence can be a serious detriment to the stall characteristics of the airfoil, while its presence, in cruise, acts like a seal that reduces drag.

A large overhang requires the overlapping skin (trailing edge lip) to be removed. Otherwise, the leading edge of the flap will strike it and prevent further deflection. On the other hand, if the overhang is larger than the hingeline radius of the flap, the leading edge will translate with deflection as shown in Figure 10-26, and the associated (and inevitable) large gap. The presence of this gap is remedied on the Cirrus SR22 by a flexible plastic strip that is bonded to the upper surface and greatly reduces the gap size.

Aerodynamic Properties

One of the design variables is flap chord ratio. A comparison for three flap chords is provided in Ref. [13]. These are shown in Figure 10-27. Equation (10-1) is least squares fit to the data for the three flaps.

(10-1)

where δ_f is in degrees. The magnitude of the C_lmax using these equations is listed in the table below. It can be seen that a flap chord ratio of 0.20·C to 0.30·C will yield the highest value of the maximum lift coefficient. Reference [13] recommends 0.25·C as the optimum flap chord. The highest C_lmax of the flap is obtained when it is deflected 60°. The magnitude of the C_lmax was not found to vary much within the range of Reynolds numbers tested (0.6 × 10⁶ to 3.5 × 10⁶). Drag coefficients were shown to increase rapidly once the lift coefficient exceeds 1.2, which can be attributed to the increased flow separation behind the flap.

Another aerodynamic issue is the influence of a gap between the flap and the main wing. Such a gap allows air to flow from the higher pressure on the lower surface to the upper one. This reduces the effectiveness of the flap, as is clearly shown in Figure 10-28. At a deflection of 60°, the maximum lift coefficient drops from about 2.02 to 1.65 in the presence of a 0.0032·C gap. Other data can be seen in Table 10-2.

Split Flap

The split flap is a simple flap concept that, like the plain flap, is deflected through rotation only (see Figure 10-29). It was invented in part by Orville Wright [16] and James M. H. Jacobs, who patented it jointly in 1924 under US Patent 1,504,663. Typical deflection angles range from 0° to 70°. The flap is very simple mechanically. When deployed it enlarges and magnifies the high-pressure region on the lower surface of the wing ahead of the flap, while generating a large separation region behind it. It provides great attitude and glide-slope control due to the high increase in drag without too much increase in lift or pitching moment. When used as a speed brake, it is superior to a spoiler (which is operated on the upper surface) because it increases drag without the lift reduction – it actually increases lift, but sharply reduces the L/D ratio, making the approach easier to control. The increase in C_lmax is low compared to more sophisticated flap types (although arguably it is surprisingly high) and for that reason the flap is not used on any modern airliner. However, it is used on the Douglas DC-3 (C-47) aircraft and on many fighter and bomber aircraft operated during WWII: for instance, the Curtiss SB2C Helldiver and Douglas SBD Dauntless dive bombers, both of which featured split flaps with a large number of holes to reduce buffeting effects [17]. Among GA aircraft featuring the flap is the Cessna 310 and the Yakolev Yak-18T.

Zap Flap

The Zap flap is a variation of the split flap that introduces translation in addition to the rotation (see Figure 10-30). It gets its name from inventor Edward F. Zaparka, who patented it in 1933 as US Patent 2,147,360. In its simplest implementations, an actuator or a pushrod will force the leading edge of the flap backward. The presence of a special linkage forces the device to simultaneously rotate into position, increasing the chord. On a wing, it increases the wing area. As a consequence, the Zap flap generates higher lift than the split flap. The flap has not seen commercial use, but was tested in the late 1930s and early 1940s by NACA using Fairchild 22 [18] and Fairchild XR2X-1 [19] aircraft. Some results are presented below.

General Design Guidelines

Split flaps of either kind may cause severe buffeting if deployed at high airspeed, for instance when used as a dive brake. The solution is to fabricate the flap with perforations. The hinge moment of the Zap flap may reverse if there is an enlargement of the gap between the wing and the leading edge of the flap as a consequence of the flap’s translation and rotation.

Aerodynamic Properties

The split flap increases C_lmax by a value ranging from 0.66 to 1.05, depending on airfoil, chord, and deflection. Generally it is deflected to an angle of 60°. The references cited showed the stall AOA to change from −1.2° to −7.2°. The change in C_m is −0.16 to −0.19. The zero AOA drag coefficient changed by some 0.1512.

The author has been unable to locate wind tunnel test data for specific airfoils featuring a Zap flap. The Zap flap was tested on a full-scale aircraft in 1942. A deployment of both the split and Zap flap leads to a relatively small shift in the stall AOA, in particular the Zap flap, which had a marginal increase in the stall AOA (which is very unusual for trailing edge high-lift devices) according to Refs [18,19].

Reference [19] found the Zap flap to increase maximum lift coefficient by 1.08 for a configuration that had a gap of 0.010C between the wing and the flap leading edge. The same flap with a gap of 0.037C increased this by 0.20. The minimum drag coefficient increased by 0.11 and the pitching moment coefficient decreased by −0.225. Other data can be seen in Table 10-2.

The data for the Zap flap pertains to a three-dimensional wing, rather than an airfoil, like the other devices in this chapter. The wing of the test vehicle had a constant chord of 4.34 ft, wingspan of 33.02 ft, and wing area of 141.5 ft², giving it an AR of 7.705.

General Design Guidelines

Loads are reacted by flap hinges that are mounted externally. These should be aerodynamically faired, even though this appears not to have been a concern in the design of the Ju-52. The flap was investigated by NACA in 1935 and 1936. NACA TN-524 [20] found the ideal hinge location to be 0.0125·C (1.25%) behind the trailing edge and 0.025·C (2.5%) below the chord line. These dimensions are referred to as x_f and y_f in Figure 10-31. NACA R-541 [21] also presents similar results, where it was remarked that this position is quite critical. The flap must be neutrally balanced, or slightly nose-heavy about the hinge line to prevent flutter. If the hingeline of the flap is close to its leading edge, an external installation of flap balance will be required and this will further increase the drag of the design.

Aerodynamic Properties

Reference [20] wind tunnel tested a Junkers flap configuration featuring a Clark Y airfoil for the main wing element and NACA 0012 for the flap element. The C_lmax of the flap in the optimum location was found to equal 1.81, based on the total area, which included the combined area of the test wing element and the flap. This compares to 1.250 for the basic Clark Y at the test R_e of 0.609 × 10⁶. Therefore, the increase in C_lmax amounts to merely 0.56. The minimum drag of the baseline airfoil presented in the report was 0.0155, but this was shown to be reduced to 0.0146 by deflecting the flap −5° (TEU). Furthermore, a deflection angle of +5° (TED) is suggested for use during climb.

Reference [21] investigated the use of a Junkers flap using a NACA 23012, 23021, and Clark Y basic airfoils. The flap chord tested was 0.20·C and 0.30·C. The resulting aerodynamic effects can be found in Table 10-2. As one would expect, it found the optimum flap location to vary based on the airfoil, although not far from the position determined by Ref. [21].

General Design Guidelines

Some forethought must be exercised when laying out the hinge geometry. If the highest point on the flap is ahead of the hingeline when stowed, it will travel to an even higher point as it is being deployed. This may cause the flap to bind or jam in the cove, either during deployment or during retraction. This problem is compounded by the fact that the flap will flex upward when loaded. This may cause the flap to jam in flight, even if no such problems are evident on the ground. Therefore, the flight test team should try to emulate the flap flexing on the ground to avoid the problem in the air. A jammed flap may be a nuisance that requires the airplane to return to base for a repair. This is the most likely scenario. However, it is also possible it would result in a more serious flap asymmetry if the control system was fabricated such the flap on one side of the plane of symmetry could deploy fully with the other one partially deployed.

Since the presence of the slot entry (or cove entry) increases drag, there are variations of this flap that feature a cove panel to open and close it via special slave linkage. An example is shown in Figure 1.10 of Ref. [8]. The flap system should be capable of deflecting to approximately 40°, as shown in Figure 10-34. Exceeding this has limited value and may actually aggravate stall characteristics. For smaller airplanes such added complexity should be avoided. However, sealing the cove is recommended, as shown in Figure 10-36. It reduces drag considerably at typical cruise lift coefficients.

Another issue frequently overlooked is one of actuation binding, which can be caused by very high friction in the flap actuation system. Actuation binding is a serious issue as the actuation motor may not have the power to overcome the friction. It also flexes the structure and is a fatigue issue waiting to happen. It is usually a result of multiple hinges, whose hinge points are not perfectly concentric or mounted on poor foundations (e.g. flexible brackets mounted to plates rather than stiff frames and bulkheads).

Recall that at least two hinges must be used for this flap. Often, in order to minimize flap flex, three or more hinges are necessary. Mathematically, the hingeline must be a straight line that goes through all the hinges – one must be able to simultaneously look through all the hinge-holes. This means that a tight tolerance must be associated with their location – and often the only way to mount the flap is through a high-precision match drilling after the flap hinges have been installed. It is not recommended to pre-drill the hinges as their installation will not guarantee the hinge points are on the same mathematical line.

Aerodynamic Properties

The presence of the slot entry is required on the lower surface of the airfoil. This increases the drag of the airfoil with the flap stowed (see Figure 10-36) by approximately 10 drag counts (i.e. 0.0010). This should be considered the cost of doing business. The expected increase in lift, ΔC_lmax, should be a fairly good 0.6 to 1.0, depending on geometry and Reynolds number.

A round slot entry is recommended, although it is slightly harder to manufacture. The cost of doing business can be kept down by providing a gap seal. It does not have to be like the rubber seal indicated in Figure 10-36; it can also be a carefully sculpted wing trailing edge that practically contacts the upper surface of the flap. The drawbacks of this configuration are that the paint on the flap surface may be scraped off (can be solved with a ultra-high-molecular-weight polyethylene tape, which has a high abrasion tolerance); and that the tight fit of the upper surface of the flap to the wing on the ground may become an extremely tight fit in the air, making retraction or extension all but impossible.

The airflow through the slot is not necessarily smooth, although one would think so at first glance – this depends on the slot geometry. However, an appropriate location for a rubber seal should not be an obstruction to the flow.

Fixed-vane Double-slotted Flap

The fixed vane double-slotted flap (see Figure 10-37) is a version of the slotted flap in which the flow separation over the flap element is delayed by a fixed vane placed in front it. The explanation for why the fixed slot prevents the aft (or main) flap element from stalling is provided by the vortex analogy of Section 10.2.5, The leading edge slat. A vortex placed at the leading edge of each segment reduces the pressure peak, delaying the flow separation.

The configuration increases the maximum lift of the slotted flap, but it is heavier and costlier to manufacture. However, it is lighter and less expensive than its articulating cousin, to be discussed next. The vane allows the main flap to be deflected to an angle as high as 55° before suffering reduced improvement in C_Lmax. The configuration increases drag over that of the single-slotted flap, even at lower deflection. This is remedied by the mechanically more sophisticated articulated vane, which is closed at low flap deflections to reduce drag and improve T-O and climb performance. The fixed vane is used on the McDonnell Douglas DC-9/MD-80 commercial jetliner, the Hondajet and the Cirrus SF50 Vision prototypes.

Articulating-vane Double-slotted Flap

There are two primary advantages of using an articulating vane for a double-slotted flap (see Figure 10-38). First, the actuation of the flap can be such that the vane closes the slot between it and the flap’s main element. This reduces the drag of the configuration, helping to improve T-O and climb performance. Second, the articulation allows an increase in the total chord over that of the fixed vane with no increase in stowed space requirements. This way the Fowler motion of the flap can be increased, which increases the maximum lift coefficient of the configuration.

The primary drawback of the articulating vane is its mechanical complexity and weight. The vanes are usually spring-loaded and rest up against a stop. Once the main element has transited backward a certain distance, the vane slot will have opened fully and the vane now begins to transit aft with the main element of the flap. The vane is attached to the flap using straight or curved tracks that are hidden in the main element.

Main/aft Double-slotted Flap

This version of the double-slotted flap is mechanically more complicated than the fixed or articulating vane flaps discussed above. This is because both elements translate and rotate (see Figure 10-39). The chord increase due to these is also greater than that of the articulating vane, yielding a slightly higher maximum lift coefficient. The forward element is the larger of the two and is now referred to as the main element. The wing overlaps the forward element, which overlaps the aft element. The forward flap typically deflects 30° to 35° (δ_f1) whilst the aft flap deflects 28° to 30°, or through a total deflection of 58° to 65° (δ_f2).

Triple-slotted Flap

It is debatable whether to consider the triple-slotted flap a variation of the slotted flap or a Fowler flap. This is due to the large translation the flap is subjected to during transit (see Figure 10-40). Typical deflection of the front element is 30°, center element 45°, and aft element 80° (approximately). The flap increases airfoil chord length and camber, yielding a large increase in C_Lmax, C_D, and C_M. A very large increase in C_Lmax results in substantial reduction of the stalling speed of heavy aircraft. Using A. M. O. Smith’s vortex analogy [4], there is a very complex interaction of gap jet airspeeds that combine to reduce flow separation over the elements, resulting in a high C_Lmax. The drag of the configuration is high, which is helpful to the pilot during the landing phase.

It is an important drawback that a very complicated and heavy mechanical system is required to deliver each flap element to its desired position. The elements must move in harmony on either side of the plane of symmetry to avoid flap asymmetry. The flaps generate very high loads that require substantial structure to support and they subject the wing to a large torsion. The flaps cause a large increase in drag, which may require high engine thrust to overcome. This can cause handling complaints if the engine spool-up time is slow. Even though the triple-slotted flap generates higher section lift coefficients than the double-slotted flap, once in three-dimensional flow it suffers from greater losses due to the flap tip vortices. The flaps result in a very large increase in pitching moment, which must be arrested by powerful stabilizing surfaces. From an operational standpoint, the mechanical system requires increased labor hours for maintenance.

Triple-slotted flaps are primarily used for commercial jetliners. Among aircraft featuring the flap are the Boeing B-727, 737, and 747. Recent advances in computational fluid dynamics (CFD) have resulted in a reduction in wing sweep that, in turn, has reduced the need for such complex flaps. Jetliners such as the 757, 767, and those made by Airbus feature the main/aft double-slotted flaps.

General Design Guidelines

Designing a multi-element flap usually takes scores of engineers. The complexity of such flaps should not be underestimated. Mechanically sophisticated flaps, which require translation and rotation, can pose a number of development issues in addition to those that have already been brought up, such as excessive play in the actuation mechanism that leads to a reduced deflection' Not to mention the possibility of a flutter problem. Issues often arise with the overlap and gap between the flap and the wing, which may change the maximum lift. There are issues with the positioning of the flap with respect to the wing, when deployed. The optimum location of the flap for maximum lift as predicted by Navier-Stokes solvers usually differs from that obtained in wind tunnel testing. If tight tolerances are not maintained, asymmetric flap deflection between the left and right sides may result and this can lead to roll-off problems when stalling in either the T-O or landing configuration. The motion of the flap must be such that the vane remains in contact with the upper wing skin (or upper cove or spoiler) for the first 15°, making it a less draggy single-element flap for the T-O configuration. Finally, the more sophisticated the flap, the more internal wing volume it tends to absorb. This will affect available fuel volume for selected applications and should be considered during the flap selection process.

Ideally, the flaps should actuate reliably and repeatedly for many years without jamming, requiring only routine maintenance, such as regular lubrication. As usual, when it comes to mechanical design, the simplest configuration that does the job is always the best one.

Single-slotted Fowler Flap

The single-slotted Fowler flap is generally deployed by a large translation first, followed by a rotation to as much as 40°–45° (see Figure 10-41). The translation requires the upper skin to extend much farther aft than the single-slotted flap. This means the upper aft wing skin must be stiffened in order to prevent it from bulging outward, creating a structural challenge. A single-slotted Fowler flap is used on the Boeing B-52 bomber and 747-SP commercial jetliner. A derivative single-slotted Fowler flap is used on the Cessna 152, 172, and other models under the name para-lift flaps. These translate far enough aft to justifiably be considered single-slotted Fowler flaps.

Figure 10-42 shows one way to acquire a Fowler motion for a flap design. The flap has two guide pins that move inside specially shaped flap track slots. The motion requires an actuator to move it forward and aft. That detail is left out, but can be accomplished using a linear actuator or jack-screws. The figure illustrates how the flap travels linearly about 60% of the total translation distance with merely 5° of deflection. The remaining 35° are accomplished over the remainder of the translation, resulting in substantial increase in the airfoil chord.

General Design Guidelines

A Fowler flap may present unexpected challenges. As stated earlier the upper skin that covers the flap must be stiffened to ensure it will not bulge outward due to the pressure differential between the upper and lower surfaces. This can be challenging if the flap is thick, as it will leave less thickness for structural reinforcement of the slot overlap. Play in the system can be a serious threat to the success of such flaps, as can the bending stiffness of the flap itself. These are important pitfalls. If a single actuator is used per flap side, it should be placed near the mid-span station of the flap (ideally near the center of lift). This will minimize the flap moment that could twist (or yaw) the flap around its vertical axis. Such a moment can jam the flap in the guide slots as one end moves forward (or aft), in the opposite direction to the other end. Lack of bending stiffness can flex the flap between the flap tracks so it puts undue load on the tracks or causes the flap to strike the upper surface of the wing between the tracks.

Aerodynamic Properties

Reference [24] tested two types of Fowler flaps intended for use on a GA(W)-1 airfoil; a 29% chord flap designed using a computer method developed by Lockheed Aircraft, and a 30% chord flap designed by Robertson Aircraft, a company that specialized in the manufacture and installation of STOL STCs. The smaller flap achieved a C_lmax of 3.48 on the airfoil, while a C_lmax of 3.80 was achieved by the 30% chord flap. A range of optimized flap positions based on deflection angle is presented in the reference. The performance gain is highly dependent on the gap and the overlap, with an optimum gap width of approximately 2.5% to 3.0% chord for the GA(W)-1 airfoil tested.

The flap increases the pitching moment by a significant value, or ΔC_m = −0.75. The increase in the minimum drag coefficient amounted to ΔC_dmin = 0.040, and shifted it to a higher C_l.

Among other observations made in Ref. [24], the GA(W)-1 airfoil has a prominent cusp on the aft portion of the lower surface. It was found that straightening this, as is often necessary in a production environment, led to a performance penalty at C_l > 0.8. It was also found that adding vortex generators increased C_lmax by 0.2. The vortex generators increased drag at low AOAs, but decreased it at higher AOAs. Additionally, there is a negligible change in the stall AOA.

Observation indicates that a multi-element airfoil experiences two kinds of post-stall patterns referred to as an airfoil stall or a flap stall [25] (see Figure 10-43). The airfoil stall consists of the separation located mostly on the main element, whereas the flap stall resides mostly on the flap. The appearance of these is dependent on the gap between the cove and the flap, with a wide gap leading to a flap stall. The optimum gap will lead to an airfoil stall with a flow fully attached over the flap. This yields the highest maximum lift coefficient.

General Design Guidelines

Select a suitable flap height using data from the literature, for instance Ref. [27]. Note that the flap height has great impact on the drag of the Gurney flap. Refer to Figure 10-45 and Figure 10-46 for more details.

Aerodynamic Properties

A large number of papers have been published on the Gurney flap. Liebeck [26] was probably the first to present information on the Gurney flap and to attempt to explain its effect. In the paper he cites early testing performed by Douglas Aircraft that seemed to indicate drag reduction, primarily for thick airfoils. However, many later publications indicate there is in fact a drag increase, at least for airfoil geometry, useful in aircraft. For example publications by Cavanaugh et al. [27] and Myose et al. [28], both demonstrate increase in C_Lmax and C_Dmin. Neuhart [29] presents an example of a Gurney flap that increased the airfoil drag at low values of C_L three-fold. Similar results can be found in other papers.

Reference [27] investigated the impact of varying the height of a Gurney flap on a three-dimensional wing of AR = 6 in a wind-tunnel test whose results are presented below. The impact on lift, drag, and pitching moment observed gives a good insight into the effectiveness and shortcomings of the flap. In short, the results show that Gurney flaps increase C_Lmax and C_Lo (or decreases α_ZL). Furthermore, they increase C_Dmin, C_mo, and C_mα. Reference [29] presented pressure measurements on the upper and lower surfaces and found it to decrease on the upper surface and increase on the lower surface. This is consistent with an increase in flow circulation.

The impact on lift and drag is shown in Figure 10-46 and Figure 10-45. The latter figure also shows a schematic of the flow field around the trailing edge and how the presence of the flap changes the circulation around the airfoil by shifting the wake downward. The formulas shown in the graphs are obtained using quadratic least squares fit to the published data. They can be used to get an idea about the effect of the Gurney flap for new aircraft design. Note that these results are valid for wings of AR = 6 at a R_e of 1.95 × 10⁶ and should be used with care for wing shapes and flight conditions that deviate greatly from those.

An effort has been made to reduce the drag of the Gurney flap. For instance, Vijgen et al. [30] patented a serrated trailing edge for this purpose. Mayda and van Dam [31] proposed a Gurney flap with slits. The common denominator in these designs is that the reduction in minimum drag is accompanied by a drop in the maximum lift.

How to Use the Tables

Remember that the tables are intended to get you “in the ballpark” during the conceptual design phase. Airfoil; flap type and chord; and the Reynolds number at the flight condition must be known. Begin by locating the part of the table containing the type of trailing edge flap. Make note of the airfoil and Reynolds number used during the wind tunnel testing, as well as the flap chord and deflection. These are important values to keep in mind if the geometry and operational conditions of the target flap deviate significantly from these values. For values relatively close, it is acceptable to prorate the characteristics of interests (e.g. see Example 10-1 or 10-2). The values to be extracted are ΔC_lmax, Δα_max, ΔC_dmin, and ΔC_m. Also, make note of the geometry details shown in Figure 10-47 and Figure 10-48, which must be defined for proper referencing in Table 10-2.

Partial Span Flaps

Figure 10-50 shows the spanwise distribution of section lift coefficients with partial span flaps deflected 0°, 10°, 20°, and 30°. It is based on potential flow theory. The figure shows that the spanwise change in C_l over the wing is not instantaneous, but gradual. The coefficients begin to rise well outside the flap’s root and tip. This is caused by the increased circulation around the flap, which increases the upwash in the flow field outside the flap ends. The figure also shows how the upwash complicates stall tailoring efforts, as the increase in section lift coefficients on the outboard wing will cause early flow separation in that area of the wing.

Full Span Flaps – Flaperons

Full span flaps, as the name implies, extend from the inboard wing to the wingtip. Such devices substantially increase the total lift capability of the wing, although they may introduce new problems not present in the unflapped wing. First, in order to maintain roll control, aileron functionality must be introduced to the flap control system. This is usually solved by splitting the flap into inboard and outboard segments. Then, the outboard segment is designed to function as both a flap and an aileron. Such a control system configuration is referred to as flaperons.

A second drawback stems from the fact that, when deployed, the overall spanwise distribution of section lift coefficients is modified (see Figure 10-51). This may cause roll instability at stall for the flapped wing, even when there are none present for the unflapped configuration. The problem is compounded by the fact that roll control requires one flaperon to be deflected to an even greater angle than the rest of the flap. This can lead to premature aileron stall at low speeds and high AOA, just when they are needed the most. The de Havilland of Canada DHC-6 Twin Otter is an example of an aircraft that features such flaps and solves this by varying the deflection of the flaps. This is readily evident from its TCDS [32], the deflection of its double-slotted flaps varies as shown in Table 10-3.

Thus, while the aft inboard trailing element deflects to 62.5°, the aileron (which is the trailing element of the outboard flap) is limited to 26° + 17.5° = 43.5°. Helped by the presence of a slot in the flap, flow separation is kept to a minimum. A third drawback is adverse yaw. The down-deflected aileron element, of course, is associated with the wing that rolls up and this adds substantial drag to the outboard wing. The opposite happens on the wing that rolls down; comparatively substantial reduction in drag. The combination may cause a noticeable adverse yaw that must be eliminated by assertive rudder deflection.

Estimation of the Maximum Lift Coefficient

The following expression, in effect, is the BET variation used to estimate the maximum lift coefficient:

(10-2)

where

The factor 0.9 is used to account for three-dimensional effect. It is imperative to account for the detrimental effects of hingeline sweep. Note that even straight-tapered wings will be subject to it, unless of course the planform is laid out such that the hingeline is perpendicular to the plane of symmetry.

Estimation of the Pitching Moment Coefficient

Since the pitching moment of an airfoil, effectively, is the product of the lift it generates and its location on the airfoil, it is possible to approximate the total pitching moment of the wing in a manner similar to that presented in Equation (10-2):

(10-3)

where

Aerodynamic Effectiveness of Wingtips

An important element in the installation of wingtip devices is an evaluation of their effectiveness. Low-speed characteristics, such as claims of improvements in stall handling, are difficult to measure. Any anecdotal claims of this must be regarded with great skepticism, in particular if they are associated with the marketing of aftermarket products. High-speed effectiveness is easier to measure and this is usually done by measuring the impact on lift-induced drag. This allows effectiveness to be stated in terms of something relatively easy to relate to, such as an effective change in AR, denoted by ΔAR. Thus, the value of a specific wingtip device can be evaluated by accounting for it when estimating drag in performance analyses. This can be done by simply adding ΔAR to the reference AR in the standard aircraft drag model (see Chapter 15, Aircraft drag analysis).

In real applications, the addition of a wingtip device affects more than just the lift-induced drag. For one, it always adds surface area and, thus, it increases wetted area. Additionally, some wingtips, such as endplates, also increase interference drag. An example of the combined effect of installing a typical winglet is presented in Figure 10-71. The cost of reduction in the lift-induced drag usually comes at a cost of higher parasitic drag. Since the parasitic addition is so highly dependent on the aircraft itself, we will only consider the effect on the lift-induced drag here. The goal is to modify the lift-induced drag as follows:

(10-4)

where AR is the aspect ratio of the original (or baseline) wing, C_L is the lift coefficient at some reference flight condition, and e is the Oswald span efficiency of the original wing. Assume further that we modify the baseline wing by mounting a wingtip device, whose addition to the wingspan is given as Δb_t at each wingtip. While this increases both the wingspan and wing area, we will consider both the reference span and area to be unchanged. Additionally, we consider the difference in the Oswald efficiency of the two wing styles to stem solely from the addition of some finite aspect ratio, ΔAR, to the baseline AR. This can be justified based on the observation that as far as lift-induced drag is concerned, it is the product AR·e that matters and not AR or e on its own. Therefore, we can either modify AR, or e, or the product of the two. Here, however, for convenience, we will consider this change in terms of the AR as it is easier to relate to, as stated above. The gain in AR is calculated from:

(10-5)

Derivation of Equation (10-5)

The purpose of the formulation is to apply it to an airplane being operated at some desired C_L so the wingtip style being considered can be compared to the baseline wing. For this reason, we can specify the two following condition at some given lift coefficient, C_L:

This shows that the difference in lift-induced drag is given by:

Solve for ΔAR:

QED

Gain in effectiveness:

Gain in effectiveness: ΔAR = −0.18

Gain in effectiveness: ΔAR = +0.004

The Upturned Booster Wingtip

The upturned booster wingtip consists of geometry in which the lower and upper surfaces join in a sharp termination, or edge, that flares upward at the trailing edge, as shown in Figure 10-61 and Figure 10-62. The wingtip style is most easily made from composite materials, although the sharp edge sometimes requires fabrication techniques that minimize the formation of production nuisances such as dry fibers and “bridging.”

Theoretically, the wingtip increases the separation of the wingtip vortices and, therefore, increases the effective AR. In practice, the increase is probably negligible. It also increases dihedral effect by a small amount.

The Downturned Booster Wingtip

The downturned booster wingtip is effectively an inversion of the upturned style. Just like the upturned booster tip, there is not much to be found in the literature regarding improvements in effectiveness (e.g. see Rokhsaz [37]). Naik and Ostowari [38] present an experimental investigation of several non-planar wingtip configurations, including a downturned droop. The results provided show limited to no benefit over the planar reference wing. In accordance with standard lateral stability theory, the downturned booster wingtip decreases dihedral effect, i.e. roll stability. However, there is a perception they improve handling near stall and, thus, have been marketed as a part of short t-o and landing (STOL) STCs for low-speed aircraft. Other schools of thought claim they have a detrimental effect on spin characteristics as a low-pressure region is formed around the wingtip, which will help drive autorotation and, thus, can render spin recovery more difficult.

Gain in effectiveness: ΔAR = 0.00

Rakelet

The Rakelet is a combination of the raked wingtip and a winglet, and is considered a new wingtip device. Investigated as a proposal for the KC-135 Stratotanker, by Diaz et al. [40], it is claimed to improve its range over that of the baseline wing by as much as 7.5%.

The Whitcomb Winglet

The development of the Whitcomb winglet (see Figure 10-73) is attributed to Richard T. Whitcomb (1921–2009), who in the early 1970s conducted research with his team of scientists in the Langley 8-foot Transonic Pressure Tunnel [47]. Part of this work was published in 1976, in a NASA report he authored [48]. It marks the first time a winglet was seriously considered for a large and heavy aircraft. Once this pioneering work demonstrated winglets were indeed effective, NASA began to conduct a substantial amount of research on the topic. Reference [49] was the first in a long line of technical papers evaluating its capabilities resulting from this effort. In the late 1970s, Whitcomb developed a winglet for use on a Boeing KC-135 tanker aircraft. The research showed the winglet increased its cruise range by as much as 7% [50]. This work encouraged many manufacturers of commercial, business, and GA aircraft to produce aircraft with winglets. The Gates Learjet Model 28/29 Longhorn was the first production airplane to feature winglets (although these had the lower winglet omitted). A Whitcomb winglet was also featured on the Rutan VariEze designed in 1974. The Boeing 747-400 was the first commercial jetliner produced with winglets.

A flight test evaluation of a Whitcomb winglet on the McDonnell-Douglas DC-10 commercial jetliner in the early 1980s revealed that the most efficient configuration consisted of a combination of a slight aileron droop with a reduced span winglet. The combination reduced fuel burn at cruise by 3%, increased range by 2%, and reduced T-O distance by 5% at maximum gross weight [51]. In 1990, McDonnell-Douglas began deliveries of MD-11s with such a winglet installed. The winglet differed from the basic Whitcomb type in that it had a lower AR and started much closer to the leading edge of the wing (see Figure 10-74).

Reference [48] compared lift, drag, and pitching moment of a wind-tunnel model of the KC-135 with three wingtip devices attached: a wingtip extension of 38% of the height of the upper winglet, the upper winglet, and the upper and lower winglets combined. The results for drag are reproduced in Figure 10-75. It shows that the winglet generates less drag than simply extending the wingtip. It also shows that the drag reduction obtained by the upper and lower combination is no better than with only the upper winglet. This has resulted in a modification to the general Whitcomb design, to be discussed next. Strictly speaking, the smaller winglet does not have to be smaller – it is just so to prevent it from striking the ground on low-wing aircraft [48, p. 8].

The Blended Winglet

The blended winglet differs from the Whitcomb winglet in the absence of the lower winglet. As can be seen in Figure 10-75, the drag benefit of the Whitcomb winglet is marginal at low (cruise) lift coefficients to say the least. Comparing this contribution to the manufacturing complexity and weight, it is reasonable to simply remove it. Another difference between the two is the generous arc of the intersection between the wing and the winglet. This allows the wing airfoils to transition smoothly to the winglet airfoils. It also replaces the sharp intersection of the Whitcomb winglet, reducing the pressure peak and, therefore, local airspeeds. Keeping those low is important in preventing flow separation due to low-pressure peaks (interference drag) and the formation of normal shock at high Mach numbers (wave drag).

The blended winglet can be seen on many modern airliners. The most visible aircraft include aircraft such as the Boeing 737, Boeing 757 (see Figure 10-76), and many others.

The blended winglet was designed and patented by Louis B. Gratzer as U.S. Patent 5,348,253. The patent states the theoretical background behind the design, where it is intended to solve a common deficiency of winglet installation – sharp discontinuities of intersections that result in departure from optimum loading. This is resolved using the gradual transition of the blended geometry, which allows the wingtip airfoil geometry to change smoothly to that of the winglet. It was specifically selected by Boeing due to fewer changes being required to the existing airframe [52]. Some pros and cons of winglets are presented in Table 10-7.