  How to determine accurately and efficiently the aerodynamic forces of the
aircraft in high-speed flow is one of great challenges in modern aerodynamics.
In this Letter we propose a new similarity law for steady transonic-supersonic
flow over thin bodies. The new similarity law is based on the local Mach number
frozen principle. It depends on both the specific heat ratio and the
free-stream Mach number. The new similarity law enables one to determine the
lift and drag coefficients of the aircraft from that of a reference state which
is more reachable. The validity of the new similarity law has been confirmed by
the excellent agreement with numerical simulations of both two-dimensional
airfoil flows and three-dimensional wing flows.
