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The acoustic analogy is used to derive far-field radiation equations for high-speed propellers in flight via a helicoidal surface representation of the blades. The linear thickness and loading sources and the nonlinear quadrupole sources are steady in blade-fixed coordinates. Blade sweep and off set (bending normal to the chord) appear explicitly as phase lag effects. The frequency domain results clarify the role of acoustic noncompactness, i.e., noise cancellation due to finite chord and span effects. The analysis extends, unifies, and refines the theories of several previous workers. The theory agrees well with data from a supersonic tip speed propeller.
Donald B. Hanson (Wed,) studied this question.