Winglets

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A recent development that holds some promise for reducing induced drag, short of increasing the aspect ratio, is the so-called winglet. The details of a winglet (studied in Ref. 4.15) are shown in Figure 4.35; Figure 4.36 pictures the winglet mounted on the wing tip of a first-generation jet transport (such as a Boeing 707).

The winglet is reminiscent of the tip plate, which has been tried over the years for the same purpose. These plates have never proven very successful for reasons that will become clear as the details of the winglet design are discussed.

Placing the winglet on an existing wing will alter the spanwise dis­tribution of circulation along the wingspan and hence the structure of its trailing vortex system far downstream. One can calculate the reduction in the induced drag afforded by the winglet solely by reference to the ultimate wake, or so-called Treffetz plane. This is the method used by Reference 4.17 together with a numerical vortex-lattice, lifting-surface theory. Examining only the ultimate wake is not very satisfying, however, from a physical standpoint. Instead, consider the flow field into which the winglet is inserted.

Figure 4.36 NACA model of first-generation jet transport with tip-mounted winglets.

Figure 4.37 qualitatively illustrates the situation. Outboard of the tip, the flow is nearly circular as air from beneath the wing flows outward along the span, around the tip, and inward on the upper surface. The velocities induced by the wing are shown. To these the free-stream velocity is vectorially added. The magnitudes of the induced velocities generally increase toward the tip. At a given spanwise location, the induced velocities are highest close to the surface of the wing, just outside of the boundary layer.

Consider a section of the winglet as shown in Figure 4.37c. The induced velocity Vi produced by the main wing combines with the free-stream velocity, V, to produce an angle of attack, a. Assuming a to be a small angle, a net forward component of force, – dD, results from the differential section lift and drag on the winglet. Denotin^winglet quantities by a subscript w,

— dD = dLwaw — dDw

Observe that the same result is obtained if the winglet is mounted below the wing, where the induced velocity is outward.

Since we do not know the induced flow in sufficient detail to integrate along the span of the winglet, let us assume an average 17,- acting over the

figure 4.37 Generation of negative drag by winglet section, (a) Looking in direction of flight. (b) Planview. (c) Forces acting on winglet.

The induced angle, aw, must be proportional to CL. Therefore let

aw = KCL

Also, approximately,

Cr =277

Therefore, Acd becomes

This approximate analysis indicates that:

1. The reduction in CD increases linearly with Cl-

2. At low CL values, CD will be increased by the addition of a winglet.

3. High winglet aspect ratios are desirable.

The severe limitations inherent in the assumptions leading to Equation 4.54 must be recognized. For a given value of SJS, it would appear that increasing Aw would always result in a greater reduction of Co – This is not true, since increasing the winglet span will result in a smaller constant of proportionality, K. The same can be said for increasing SJS. Despite these limitations, the foregoing discloses the basic elements that are necessary for the design of an effective winglet. Its profile drag (including interference with the wing) must be low. Its aspect ratio should be fairly high to assure a high lift curve slope and low induced draggfor the winglet. Not as apparent, the winglet should be mounted as near the trailing edge as possible in order to experience the highest induced velocities possible for a given wing CL■ Also, in this regard, a winglet would be expected to produce a larger decrement in CD for a wing having a relatively higher loading near its tips.

Figure 4.38 presents experimental measurements of ДCd as reported in References 4.15 and 4.16. In the case of the second-generation jet transport

Figure 4.38 Effect of winglets on drag of first and second-generation jet trans­ports.

(such as a DC-10), the loading is relatively lower near the wing tips, so the winglets are less effective. As predicted, ДCD is seen to vary nearly linearly with CL2. In the case of the first-generation jet transports, a decrement in CD is achieved for CL values greater than 0.22. This number increases to 0.30 for the second-generation jet transports.

The induced drag of a wing can also be reduced simply by extending its tip and thereby increasing its aspect ratio. Reference 4.17 considers this possibility and compares the savings in drag to be gained from extending the tips with those obtained by the use of winglets. Since either method will result in greater root bending moments and hence increased wing structure and weight, both the induced drag and wing root bending moments are treated by tiie reference. Typical results from this study are presented in Figure 4.39. It is emphasized that these results are from potential flow calculations and thus do not include the profile drag of the winglet or any interference drag. The trends determined by the reference are probably valid but somewhat optimis­tic with regard to the winglets. For identical increases in bending moment, the winglet can provide a greater reduction in induced drag than can be achieved with a tip extension. Referring to Figure 4.39, the ratio «with/^without is simply

Mr. with /МГі without Figure 4.39 Comparison of tip extension and winglet when added to an un­twisted wing.

the ratio of the induced drag coefficient of the original wing to the coefficient with a winglet or tip extension. Consider, for example, an untwisted wing with an aspect ratio of 8 and a taper ratio of 0.5. The leading edge, as with all the wing studies in Reference 4.17, is swept back 30°. With a winglet, the induced drag can be reduced by 24% with only a 2.6% increase in bending moment. For the same bending moment increase, extending the tip would save only 6% in the induced drag. To achieve the same reduction in the induced drag with a

tip extension as with the winglet would require a 13% increase in the bending moment.