This paper focuses on the radiation modes and efficiency of propeller tonal noise. The thickness noise and loading noise model of propellers has been formulated in spherical coordinates, thereby simplifying numerical evaluation of the integral noise source. More importantly, the radiation field can be decomposed and projected to spherical harmonics, which can separate source-observer positions and enable an analysis of sound field structures. Thanks to the parity of spherical harmonics, the proposed model can mathematically explain the fact that thrusts only produce antisymmetric sound waves with respect to the rotating plane. In addition, the symmetric components of the noise field can be attributed to the thickness, as well as drags and radial forces acting on the propeller surface. The radiation efficiency of each mode decays rapidly as noise sources approach the rotating centre, suggesting the radial distribution of aerodynamic loadings should be carefully designed for low-noise propellers. The noise prediction model has been successfully applied to a drone propeller and achieved a reliable agreement with experimental measurements. The flow variables employed as an input of the noise computation were obtained with computational fluid dynamics (CFD), and the experimental data were measured in an anechoic chamber.

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