Transonic Airfoil Design

The transonic airfoil design problem arises because we wish to limit shock drag losses at a given transonic speed. This effectively limits the minimum pressure coefficient that can be tolerated. Since both lift and thickness reduce (increase in magnitude) the minimum C_p, the transonic design problem is to create an airfoil section with high lift and/or thickness without causing strong shock waves. One can generally tolerate some supersonic flow without drag increase, so that most sections can operate efficiently as "supercritical airfoils". A rule of thumb is that the maximum local Mach numbers should not exceed about 1.2 to 1.3 on a well-designed supercritical airfoil. This produces a considerable increase in available C_l compared with entirely subcritical designs.

Supercritical sections usually refer to a special type of airfoil that is designed to operate efficiently with substantial regions of supersonic flow. Such sections often take advantage of many of the following design ideas to maximize lift or thickness at a given Mach number:

Carry as much lift as is practical on the aft potion of the section where the flow is subsonic. The aft lower surface is an obvious candidate for increased loading (more positive C_p), although several considerations discussed below limit the extent to which this approach can be used.
Make sure that sufficient lift is carried on the forward portion of the upper surface. As the Mach number increases, the pressure peak near the nose is diminished and without additional blunting of the nose, possible extra lift will be lost in this region.
The lower surface near the nose can also be loaded by reducing the lower surface thickness near the leading edge. This provides both lift and positive pitching moment.
Shocks on the upper surface near the leading edge produce much less wave drag than shocks aft of the airfoil crest and it is feasible, although not always best, to design sections with forward shocks. Such sections are known as "peaky" airfoils and were used on many transport aircraft.
The idea of carefully tailoring the section to obtain locally supersonic flow without shockwaves (shock-free sections) has been pursued for many years, and such sections have been designed and tested. For most practical cases with a range of design CL and Mach number, sections with weak shocks are favored.

One must be cautious with supercritical airfoil design. Several of these sections have looked promising initially, but led to problems when actually incorporated into an aircraft design. Typical difficulties include the following.

Too much aft loading can produce large negative pitching moments with trim drag and structural weight penalties.
The adverse pressure gradient on the aft lower surface can produce separation in extreme cases.
The thin trailing edge may be difficult to manufacture.
Supercritical, and especially shock-free designs often are very sensitive to Mach and C_L and may perform poorly at off-design conditions. The appearance of "drag creep" is quite common, a situation in which substantial section drag increase with Mach number occurs even at speeds below the design value.

The section with pressures shown below is typical of a modern supercritical section with a weak shock at its design condition. Note the rooftop C_p design with the minimum C_p considerably greater above C_p*.