Compressibility Effects of Extended Formation Flight

Aircraft own in formations may realize signi cant reductions in induced drag by ying in regions of wake upwash. However, most transports y at transonic speeds and compressibility e ects in formation ight are not well understood. This study uses an Euler solver to analyze the inviscid aerodynamic forces and moments of transonic wing/body con gurations ying in a 2-aircraft formation. We consider formations with large streamwise separation distances (10-50 wingspans) in an arrangement we term extended formation ight. Compressibility-related drag penalties in formation ight may be eliminated by slowing 2-3% below the nominal out-of-formation drag divergence Mach number, at xed lift coe cient or xed altitude. The latter option has the additional bene t that the aerodynamic performance of the formation improves slightly at higher lift coe cients. Optimal in-formation lift coe cients are not nearly as high as those estimated by incompressible analyses, but if not limited by engine performance, modest increases in altitude can yield further improvements in aerodynamic e ciency. Increasing the lateral separation of the aircraft can allow for slightly higher cruise speeds in exchange for higher induced drag. For the con gurations examined here, a 1-2% reduction in Mach number combined with a lateral spacing increase of 5% span achieves a total formation drag savings of about 10%.