Theme A METHOD was developed for calculating forwardradiated shock waves and expansion regions of cylindrically blunted straight-entrance transonic compressor blades within constant-annulus inlet ducts. Tone noise at blade passing frequency and its subharmonics, caused by shock waves produced by blade curvature and nonuniformity, could be avoided in concept if all blades were precisely sharp, precisely straight, and precisely positioned. However, leadingedge thickness would necessarily be many orders of magnitude larger than the mean free path in air. Each blade, therefore, must support a detached curved wave that decays from a normal shock towards a Mach wave. It was shown by Morfeyl that if a transonic compressor generated a periodic pressure system, the upstream asymptotic pressure field was a periodic sawtooth pattern whose strength was independent of blade shape and initial shock wave strength. This prediction has been validated analytically2 and by numerical experiments3 for sharp, curved blades. It was not obvious how, or if the pressure pattern generated by straight, parallel, very slightly blunted blades would approach the same amplitudes. Contents An earlier solution4 had assumed that each detached shock wave had the shape of a hyperbola asymptotic to a Mach wave. In this solution, the strong inner-portion of each shock wave is approximated by a hyperbola with steeper asymptote. The hyperbola is matched to an isolated-blade weak-shock outer solution obtained from sonic boom theory5 for blunt two-dimensional shapes. The expansion field produced by an isolated blade's leading edge is distorted by the entropy gradient downstream of the curved strong shock. Each blade's expansion field was calculated from the sonic boom solution and corrsponds to a centered expansion whose hypothetical origin is significantly downstream of the leading edge. These portions of the solution were validated by comparisons with wind-tunnel data for isolated blunt flat plates at low supersonic speeds. Compressor cascades were represented by starting with isolated-blade shock waves and expansion regions and then calculating the upstream propagation. At moderate distances ahead of the cascade leading edge plane, the variation of static pressure with distance is given by a shock-wave compression, a linear expansion to the pressure ahead of the shock, and a region of constant pressure. Eventually each blade's shock wave overtakes the aft end of the preceding blade's expansion and the pressure pattern becomes a sawtooth waveform. As upstream distance is increased, the flowfield occurring within the expansion region. That is, the