We provided accurate estimates of distances, radii and iron abundances for four metal-rich Cepheids, namely V340 Ara, UZ Sct, AV Sgr and VY Sgr. The main aim of this investigation is to constrain their pulsation properties and their location across the Galactic inner disk. We adopted new accurate NIR (J,H,K) light curves and new radial velocity measurements for the target Cepheids to determinate their distances and radii using the Baade-Wesselink technique. In particular, we adopted the most recent calibration of the IR surface brightness relation and of the projection factor. Moreover, we also provided accurate measurements of the iron abundance of the target Cepheids. Current distance estimates agree within one sigma with similar distances based either on empirical or on theoretical NIR Period-Luminosity relations. However, the uncertainties of the Baade-Wesselink distances are on average a factor of 3-4 smaller when compared with errors affecting other distance determinations. Mean Baade-Wesselink radii also agree at one sigma level with Cepheid radii based either on empirical or on theoretical Period-Radius relations. Iron abundances are, within one sigma, similar to the iron contents provided by Andrievsky and collaborators, thus confirming the super metal-rich nature of the target Cepheids. We also found that the luminosity amplitudes of classical Cepheids, at odds with RR Lyrae stars, do not show a clear correlation with the metal-content. This circumstantial evidence appears to be the consequence of the Hertzsprung progression together with the dependence of the topology of the instability strip on metallicity, evolutionary effects and binaries.
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