High-resolution spectroscopic observations of the W UMa-type binary Epsilon CrA obtained as a time monitoring sequence on four full and four partial nights within two weeks have been used to derive orbital elements of the system and discuss the validity of the Lucy model for description of the radial-velocity data. The observations had more extensive temporal coverage and better quality than similar time-sequence observations of the contact binary AW UMa. The two binaries share several physical properties with both showing very similar deviations from the Lucy model: The primary component is a rapidly-rotating star almost unaffected by the presence of the secondary component, while the latter is embedded in a complex gas flow and appears to have its own rotation-velocity field, in contradiction to the model. The spectroscopic mass ratio is found to be larger than the one derived from the light-curve analysis, similarly as in many other W UMa-type binaries, but this discrepancy for Epsilon CrA is relatively minor suggesting a systematic problem with one of the observational methods commonly affecting other determinations. The presence of the complex velocity flows contradicting the solid-body rotation assumption suggest a necessity of modification to the Lucy model, possibly along the lines outlined by Stepien (2009) in his concept of the energy transfer between the binary components.
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