High Mach Number Difficulties
As airplanes approach and exceed the speed of sound, 761 miles per hour at sea level, the air’s compressibility changes the nature of the flow. The Mach number, the ratio of airspeed to the speed of sound, is how we keep track of these flow changes and their effects on airplane stability and control. First encountered in flight in the early 1940s, compressibility effects are still a consideration for designers of high-speed airplanes.
5.1 A Slow Buildup
Our understanding of the compressibility effects on airplane stability and control grew slowly by a buildup of theory and wind-tunnel data, with no counterpart in flight test experience for many years. The buildup in the theory started as far back as 1916, with work by Lord Rayleigh, followed by G. H. Bryan in 1918. Wind-tunnel studies started, too, but it was not for more than 20 years, or in the early years of World War II, that compressibility suddenly appeared as a stability and control problem in flight.
A key early theoretical result came from the ubiquitous Hermann Glauert, around 1927. This was the Prandtl-Glauert rule, applying to the variation of pressure coefficient with Mach number. The rule gives the pressure coefficient at any Mach number as the incompressible value, increased by a simple function of the Mach number. The Prandtl-Glauert rule was developed by the theory of small perturbations. A similar rule was developed around 1941 by Theodore Von Karman and H. S. Tsien. Their formulation is called the Karman-Tsien rule.
Early high-speed wind-tunnel tests were made in very small wind tunnels, compared with the larger sizes available for low-speed testing. Drs. Hugh L. Dryden and Lyman J. Briggs tested airfoils in a small supersonic jet in the 1920s. At NACA’s Langley Laboratory in the early 1930s, John Stack built small high Mach number wind tunnels as adjuncts to an existing pressurized low-speed wind tunnel. High-pressure air from the big tunnel was vented into a small vertical wind tunnel, downstream from the vertical tunnel’s test section.
At first, Stack and his group limited their tests to airfoils used in propellers, since at that time only propeller tips had experienced compressibility effects. By the end of the 1930s the work had broadened to include other airfoils. Pressure distributions showed a distinct upper surface discontinuity or jump, which Stack called the compressibility burble (Figure 11.1). Burble occurs at a critical airspeed at which the local surface velocity reaches the speed of sound. The local surface velocity at any point on an airfoil is the sum of the airspeed and the velocity induced by the airfoil shape. Stack reasoned that increases in the critical airspeed or Mach number could be attained through the development of airfoils that had minimum induced velocity for any given lift coefficient and thickness. This insight was the genesis of the first airfoils designed specifically for high Mach number flight.