We investigated the radio wavefront of cosmic-ray air showers with LOPES measurements and CoREAS simulations: the wavefront is of approximately hyperbolic shape and its steepness is sensitive to the shower maximum. For this study we used 316 events with an energy above 0.1 EeV and zenith angles below $45^circ$ measured by the LOPES experiment. LOPES was a digital radio interferometer consisting of up to 30 antennas on an area of approximately 200 m x 200 m at an altitude of 110 m above sea level. Triggered by KASCADE-Grande, LOPES measured the radio emission between 43 and 74 MHz, and our analysis might strictly hold only for such conditions. Moreover, we used CoREAS simulations made for each event, which show much clearer results than the measurements suffering from high background. A detailed description of our result is available in our recent paper published in JCAP09(2014)025. The present proceeding contains a summary and focuses on some additional aspects, e.g., the asymmetry of the wavefront: According to the CoREAS simulations the wavefront is slightly asymmetric, but on a much weaker level than the lateral distribution of the radio amplitude.
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