  The migration of profile sub-peaks identified in time-monitored optical
emission lines of Wolf-Rayet star spectra provides a direct diagnostic of the
dynamics of their stellar winds via a measured line-of-sight velocity change
per unit time. Inferring the associated wind acceleration scale from such an
apparent acceleration then relies on the adopted intrinsic velocity of the wind
material at the origin of this variable pattern. We develop radiative transfer
tools to characterise the Line Emission Region (LER) of the program lines,
including turbulence and line-optical depth effects. We find that
monitored-lines can be fitted well with a pure optically thin formation
mechanism, line-broadening resulting from the finite velocity extent of the LER
rather than turbulence.Our new estimates of LER velocity centroids are
systematically shifted outwards closer to terminal velocity compared to
previous determinations, now suggesting WR-wind acceleration length scales of
ca. 10-20Rsun, a factor of a few smaller than previously inferred. Based on
radiation-hydrodynamics simulations of the line-driven-instability mechanism,
we compute synthetic line profile variability for CIII5696A, for WR111 The
results match well the measured observed migration of 20-30 m/s2, However, our
model stellar radius of 19 Rsun, typical of an O-type supergiant, is a factor
2--10 larger than generally expected for WR core radii.Such small radii leave
inferred acceleration scales to be more extended than expected from dynamical
models of line driving, but the severity of the discrepancy is substantially
reduced compared to previous analyses. We conclude with a discussion of how
using lines formed deeper in the wind would provide a stronger constraint on
the key wind dynamics as well as information on the onset of wind clumping.
