Description: Long-range hypervelocity vehicles are studied in terms of their motion in powered flight, and their motion and aerodynamic heating in unpowered flight. Powered flight is analyzed for an idealized propulsion system which rather closely approaches present-day rocket motors. Unpowered flight is characterized by a return to earth along a ballistic, skip, or glide trajectory. Only those trajectories are treated which yield the maximum range for a given velocity at the end of powered flight. Aerodynamic heating is treated in a manner similar to that employed previously by the senior authors is studying ballistic missiles (NACA RM A53D28), with the exception that radiant as well as convective heat transfer is considered in connection with glide and skip vehicles. The ballistic vehicle is found to be the least efficient of the several types studied in the sense that it generally requires the highest velocity at the end of powered flight in order to attain a given range. This disadvantage may be offset, however, by reducing convective heat transfer to the re-entry body through the artifice of increasing pressure drag in relation to friction drag - that is, by using a blunt body. Thus the kinetic energy required by the vehicle at the ...