Examples of velocities measured in situ (black) and fitted results (colours) for five MCs. The labels in the top of the plots indicate the day of the MC front. Linear (in blue) and quadratic (in red) least square fits, Eq. (15), of the observed velocity are over-plotted. The model fit (in green) is an approximation of Eq. (19) (Taylor expansion to second order, so Eq. (21)). The purple vertical lines define the boundaries of the MCs and the range of the velocity fits. Two hours of data are added before and after these boundaries to show the MC context. The time origin is set at MC centre, i.e. t_c = (t_start + t_end)/2. The main characteristics of the quadratic fit are added in red font; all are in km s⁻¹ (see Sect. 3.2).