This figure illustrates the wing-span effect on induced drag for airplanes having same wing area, same lift coefficient, and same dynamic pressure.

High aspect-ratio wing.

Tip plates and tip tanks.

Planform and thickness taper.

Geometric and aerodynamic twist.

Reduction of induced drag. A square-tipped rectangular wing is almost as efficient as the elliptic wing.

##### Methods of Reducing Induced Drag

Induced drag is caused by the generation of lift. It is created by the vortices at the tip of an aircraft's wing. The magnitude of induced drag depends on the amount of lift being generated by the wing and on the shape and size of the wing. Long, thin (chordwise) wings have low induced drag; short wings with a large chord have high induced drag

How can the induced drag be reduced? One may (1) increase the span efficiency factor to as close to e = 1 as possible, (2) increase the wing span b (or aspect ratio AR), and (3) increase the free-stream velocity V¥. Induced drag is a small component at high speeds (cruising flight) and relatively unimportant since it constitutes only about 5 to 15 percent of the total drag at those speeds. But at low speeds (takeoff or landing), it is a considerable component since it accounts for up to 70 percent of the total drag.

The efficiency factor e and wing span are physical factors that may be controlled by proper design. A plane with a longer span wing (higher aspect ratio) has less induced drag and, therefore, greater efficiency. But structural considerations become a dominant factor. A very thin long wing requires a large structural weight to support it, and there comes a point where the disadvantage of increasing structural weight needed to support the increased wing span counteracts the advantage of decreased drag due to smaller vortex effects. An aircraft with a compromise aspect ratio, and which also considers factors such as fuel capacity, control characteristics, size allowances, and numerous other factors, would give the optimum performance. A survey of airplane categories shows sailplanes with an aspect ratio of 15 or more, single-engine light airplanes with an aspect ratio of about 6, and supersonic fighter airplanes with an aspect ratio of about 2.

An interesting way of reducing induced drag is by the use of tip plates or tip tanks. This arrangement tends to inhibit the formation of tip vortices. Tip plates have the same physical effect as an increase in wing span (or aspect ratio). Normally, these are not used since there are other more valuable drag reduction methods.

For a general wing, the airfoil sections may vary in three distinct ways along the wing. First, the size or chord length may change; second, the shape of the airfoil section may change as one moves along the wing, and lastly, the angles of attack of the airfoil sections may change along the wing.

Planform taper is the reduction of the chord length and thickness as one proceeds from the root (near the fuselage) to the tip section (at the wing tip) so that the airfoil sections also remain geometrically similar. (A planform is the shape of the wing as one looks down on it from above.)

Thickness taper is the reduction of the airfoil's thickness as one proceeds from the root section (the part of the wing closest to the fuselage) to the tip section. This reduction results in thinner airfoil sections at the wing tip. The chord remains constant. One notable exception to this normal taper was the XF-91 fighter, which has inverse taper in planform and thickness so that the wing tips were thicker and wider than the inboard stations.

Wings are given twist so that the angle of attack varies along the span. A decrease in angle of attack toward the wing tip is called washout whereas an increase in angle of attack toward the wing tip is called washin. Geometric twist represents a geometric method of changing the lift distribution, whereas aerodynamic twist changes lift by using different airfoil sections along the span—an aerodynamic method of changing the lift distribution in a spanwise manner. To give minimum induced drag, the spanwise efficiency factor e should be as close to 1 as possible. This is the case of an elliptic spanwise lift distribution. A number of methods are available to modify the spanwise distribution of lift. They include (1) planform taper to obtain an elliptic planform, used for the Spitfire wing, which was remarkably elliptic; (2) a geometric twist and/or aerodynamic twist to obtain elliptic lift distribution; or (3) a combination of all of these methods.

An elliptical planform is hard to manufacture and is costly. From the point of view of construction, the best type of wing is the untapered, untwisted wing. This is often used by light plane manufacturers. Surprisingly, data indicates that a square-tipped rectangular wing is very nearly as efficient as the elliptic wing, so that the gains in reduced induced drag may be insignificant. This result may be traced to the fact that, for a real wing, the lift distribution falls off to zero at the wing tips and approximates an elliptical distribution.

The wing-tip shape, being at the point where the tip vortices are produced, appears to be of more importance in minimizing tip vortex formation and thus minimizing induced drag. Taper and twist are perhaps of greater importance in dealing with the problem of stalling.

—Adapted from Talay, Theodore A. Introduction to the Aerodynamics of Flight. SP-367, Scientific and Technical Information Office, National Aeronautics and Space Administration, Washington, D.C. 1975. Available at http://history.nasa.gov/SP-367/cover367.htm