  Aims. The Baade-Wesselink method of distance determination is based on the
oscillations of pulsating stars. The key parameter of this method is the
projection factor used to convert the radial velocity into the pulsation
velocity. Our analysis was aimed at deriving for the first time the projection
factor of delta Scuti stars, using high-resolution spectra of the
high-amplitude pulsator AI Vel and of the fast rotator beta Cas. Methods. The
geometric component of the projection factor (i.e. p0) was calculated using a
limb-darkening model of the intensity distribution for AI Vel, and a
fast-rotator model for beta Cas. Then, using SOPHIE/OHP data for beta Cas and
HARPS/ESO data for AI Vel, we compared the radial velocity curves of several
spectral lines forming at different levels in the atmosphere and derived the
velocity gradient associated to the spectral-line-forming regions in the
atmosphere of the star. This velocity gradient was used to derive a dynamical
projection factor p. Results. We find a flat velocity gradient for both stars
and finally p = p0 = 1.44 for AI Vel and p = p0 = 1.41 for beta Cas. By
comparing Cepheids and delta Scuti stars, these results bring valuable insights
into the dynamical structure of pulsating star atmospheres. They suggest that
the period-projection factor relation derived for Cepheids is also applicable
to delta Scuti stars pulsating in a dominant radial mode.
