Modeling the Directivity of Wheel/Rail Radiation Using a Circular/Straight Line of Perpendicular Dipole Pairs

Former measurement investigation on the directivity of wheel/rail radiation has specified that (I) rail radiation is of dipole directivity characteristic in the horizontal direction, whilst it is only about 4 dB more directional than a monopole source in a vertical plane perpendicular to the rail; (2) the directivity of wheel radiation is close to the vertical directivity of rail radiation. The work presented in this paper intends to interpret the phenomenon. It is found that a model of a perpendicular dipole pair can explain these directivity characteristics specified by the measurement. This model naturally explains why rail radiation has different horizontal and vertical directivity characteristics and why wheel radiation is not a dipole source (at least for wheels with a curved web). The study also emphasizes that, when considering the directivity effect of a dipole source, the orientation of the dipole axis needs to be specified. Moreover when more than one dipole is concerned, a special disposition of the dipoles together with a selection of difference in their sound powers can result in a change of directivity pattern from that of a monopole to that of a dipole. Since rail radiation dominates at low speed whilst wheel radiation becomes more important at high speed, the horizontal directivity of rolling noise varies with train speed. Therefore, this work on the directivity can help with to construct a proper directivity description of rolling noise, which is important for an accurate wayside noise prediction at different train speeds.