Types of Wings and Transonic Flow

There are a number of ways of delaying the increase in drag encountered when an aircraft travels at high speeds, i.e., the transonic wave drag rise, or of increasing the drag-divergence Mach number (the free-stream Mach number at which drag rises precipitously) so that it is closer to 1. One way is by the use of thin airfoils: increase in drag associated with transonic flow is roughly proportional to the square of the thickness-chord ratio (t/c). If a thinner airfoil section is used, the airflow speeds around the airfoil will be less than those for the thicker airfoil. Thus, one may fly at a higher free-stream Mach number before a sonic point appears and before one reaches the drag-divergence Mach number. The disadvantages of using thin wings are that they are less effective (in terms of lift produced) in the subsonic speed range and they can accommodate less structure (wing fuel tanks, structural support members, armament stations, etc.) than a thicker wing.

In 1935, the German aerodynamicist Adolf Busemann proposed that a swept wing might delay and reduce the effects of compressibility. A swept wing would delay the formation of the shock waves encountered in transonic flow to a higher Mach number. Additionally, it would reduce the wave drag over all Mach numbers.

A swept wing would have virtually the same effect as a thinner airfoil section (the thickness-cord ratio (t/c) is reduced). The maximum ratio of thickness to chord for a swept wing is less than for a straight wing with the same airflow. One is effectively using a thinner airfoil section as the flow has more time in which to adjust to the high-speed situation. The critical Mach number (at which a sonic point appears) and the drag-divergence Mach number are delayed to higher values; Sweep forward or sweepback will accomplish these desired results. Forward sweep has disadvantages, however, in the stability and handling characteristics at low speeds.

A major disadvantage of swept wings is that there is a spanwise flow along the wing, and the boundary layer will thicken toward the wingtips for sweepback and toward the roots (the part of the wing closest to the fuselage) for sweep-forward. In the case of sweepback, there is an early separation and stall of the wingtip sections and the ailerons lose their roll control effectiveness. The spanwise flow may be reduced by the use of stall fences, which are thin plates parallel to the axis of symmetry of the airplane. In this manner a strong boundary layer buildup over the ailerons is prevented. Wing twist is another possible solution to this spanwise flow condition.

The wing's aspect ratio is another parameter that influences the critical Mach number and the transonic drag rise. Substantial increases in the critical Mach number (the subsonic Mach number at which sonic flow occurs at some point on the wing for the first time) occur when using an aspect ratio less than about four. However, low-aspect-ratio wings are at a disadvantage at subsonic speeds because of the higher induced drag.

By bleeding off some of the boundary layer along an airfoil's surface, the drag-divergence Mach number can be increased. This increase results from the reduction or elimination of shock interactions between the subsonic boundary layer and the supersonic flow outside of it.

Vortex generators are small plates, mounted along the surface of a wing and protruding perpendicularly to the surface. They are basically small wings, and by creating a strong tip vortex, the vortex generators feed high-energy air from outside the boundary layer into the slow moving air inside the boundary layer. This condition reduces the adverse pressure gradients and prevents the boundary layer from stalling. A small increase in the drag-divergence Mach number can be achieved. This method is economically beneficial to airplanes designed for cruise at the highest possible drag-divergence Mach number.

A more recent development in transonic technology, and destined to be an important influence on future wing design, is the supercritical wing developed by Dr. Richard T. Whitcomb of NASA's Langley Research Center. With the supercritical wing, a substantial rise in the drag-divergence Mach number is realized and the critical Mach number is delayed even up to 0.99. This delay represents a major increase in commercial airplane performance.

The curvature of a wing gives the wing its lift. Because of the flattened upper surface of the supercritical airfoil, lift is reduced. However, to counteract this, the new supercritical wing has increased camber at the trailing edge.

There are two main advantages of the supercritical airfoil. First, by using the same thickness-chord ratio, the supercritical airfoil permits high subsonic cruise near Mach 1 before the transonic drag rise. Alternatively, at lower drag divergence Mach numbers, the supercritical airfoil permits a thicker wing section to be used without a drag penalty. This airfoil reduces structural weight and permits higher lift at lower speeds.

Coupled to supercritical technology is the "area-rule" concept also developed by Dr. Richard T. Whitcomb in the early 1950s for transonic airplanes and later applied to supersonic flight in general.

Basically, the area rule states that minimum transonic and supersonic drag is obtained when the cross-sectional area distribution of the airplane along the longitudinal axis can be projected into a body of revolution that is smooth and shows no abrupt changes in cross section along its length. Or, if a graph is made of the cross-sectional area against body position, the resulting curve is smooth. If it is not a smooth curve, then the cross section is changed accordingly.

The original Convair F-102A was simply a scaled-up version of the XF-92A with a pure delta wing. But early tests indicated that supersonic flight was beyond its capability because of excessive transonic drag and the project was about to be canceled. Area ruling, however, saved the airplane from this fate. In the original YF-102A, the curve of the cross-sectional area plotted against body station was not very smooth as there was a large increase in cross-sectional area when the wings were attached. The redesigned F-102A had a “coke-bottle”-waist-shaped fuselage and bulges added aft of the wing on each side of the tail to give a better area-rule distribution. The F-102A could then reach supersonic speeds because of the greatly reduced drag and entered military service in great numbers.

Later, the area-rule concept was applied to design of a near-sonic transport capable of cruising at Mach numbers around 0.99. In addition to area ruling, a supercritical wing was used.

—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

For Further Reading:

Anderson, Jr., John D. A History of Aerodynamics. Cambridge, England: Cambridge University Press, 1997.

Bilstein, Roger E. Orders of Magnitude: A History of the NACA and NASA, 1915 – 1990. NASA NP-4406. Washington, D.C.: Government Printing Office, 1989. Also at http://www.hq.nasa.gov/office/pao/History/SP-4406/cover.html.

Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag, 1991.

“Proceedings of the F-8 Digital Fly-by-Wire and Supercritical Wing First Flight's 20th Anniversary Celebration” (May 27, 1992). NASA Conference Pub 3256, Vol. 1 at http://techreports.larc.nasa.gov/cgi-bin/NTRS (search on supercritical on the Dryden Technical Report Server).

X-29 Fact Sheet. National Aeronautics and Space Administration. Dryden Flight Research Center, April 1998. http://trc.dfrc.nasa.gov/PAO/PAIS/HTML/FS-008-DFRC.html