  In order to advance our understanding of the dynamic interactions between
coronal mass ejections (CMEs) and the magnetized solar wind, we investigate the
impact of magnetic erosion on the well-known aerodynamic drag force acting on
CMEs traveling faster than the ambient solar wind. In particular, we start by
generating empirical relationships for the basic physical parameters of CMEs
that conserve their mass and magnetic flux. Furthermore, we examine the impact
of the virtual mass on the equation of motion by studying a variable-mass
system. We next implement magnetic reconnection into CME propagation, which
erodes part of the CME magnetic flux and outer-shell mass, on the drag acting
on CMEs, and we determine its impact on their time and speed of arrival at 1
AU. Depending on the strength of the magnetic erosion, the leading edge of the
magnetic structure can reach near-Earth space up to $\approx$ three hours
later, compared to the non-eroded case. Therefore, magnetic erosion may have a
significant impact on the propagation of fast CMEs and on predictions of their
arrivals at 1 AU. Finally, the modeling indicates that eroded CMEs may
experience a significant mass decrease. Since such a decrease is not observed
in the corona, the initiation distance of erosion may lie beyond the
field-of-view of coronagraphs (i.e. 30 $\mathrm{R_{\odot}}$).
