Transonic Effects – Area Rule

At high subsonic speeds, the local velocity along a curved surface (e. g., on an aero­foil surface) can exceed the speed of sound, whereas flow over the rest of the surface

remains subsonic. In this case, the aerofoil is said to be in transonic flow. At higher angles of attack, transonic effects can appear at lower flight speeds. Aerofoil – thickness distribution along the chord length is the parameter that affects the induc­tion of transonic flow. Transonic characteristics exhibit an increase in wave drag (i. e., the compressibility effect; refer to aerodynamic textbooks). These effects are undesirable but unavoidable; however, aircraft designers keep the transonic effect to a minimum. Special attention is necessary in generating the aerofoil section design, which shows a flatter upper surface. Figure 3.22 depicts a typical transonic aerofoil (i. e., the Whitcomb section) and its characteristics.

The Whitcomb section, which appeared later, advanced the flight speed by min­imizing wave drag (i. e., the critical Mach-number effects); therefore, it is called the supercritical aerofoil section. The geometrical characteristics exhibit a round LE, followed by a flat upper surface and rear-loading with camber; the lower surface at the trailing edge shows the cusp. All modern high-subsonic aircraft have the super­critical aerofoil section characteristics. Manufacturers develop their own section or use any data available to them.

For an aircraft configuration, it has been shown that the cross-sectional area dis­tribution along the body axis affects the wave drag associated with transonic flow. The bulk of this area distribution along the aircraft axis comes from the fuselage and the wing. The best cross-sectional area distribution that minimizes wave drag is a cigar-like smooth distribution (i. e., uniform contour curvature; lowest wave drag) known as the Sears-Haack ideal body (Figure 3.23). The fuselage shape approxi­mates it; however, when the wing is attached, there is a sudden jump in volume dis­tribution (Figure 3.23). In the late 1950s, Whitcomb demonstrated through exper­iments that “waisting” of the fuselage in a “coke-bottle” shape could accommo­date wing volume, as shown in the last of Figure 3.23. This type of procedure for wing-body shaping is known as the area rule. A smoother distribution of the cross­sectional area reduces wave drag.

Whitcomb’s finding was deployed on F102 Delta Dragger fighter aircraft (see Figure 3.23). The modified version with area ruling showed considerably reduced transonic drag (see Figure 4.29). For current designs with wing-body blending, it is less visible, but designers still study the volume distribution to make it as smooth as possible. Even the hump of a Boeing 747 flying close to transonic speed helps with the area ruling. The following subsection considers wing (i. e., 3D body) aerodynamics.