The Fixed-\Phi (F\Phi) and Harmonic Mean (HM) fitting methods are two methods
to determine the average direction and velocity of coronal mass ejections
(CMEs) from time-elongation tracks produced by Heliospheric Imagers (HIs), such
as the HIs onboard the STEREO spacecraft. Both methods assume a constant
velocity in their descriptions of the time-elongation profiles of CMEs, which
are used to fit the observed time-elongation data. Here, we analyze the effect
of aerodynamic drag on CMEs propagating through interplanetary space, and how
this drag affects the result of the F\Phi and HM fitting methods. A simple drag
model is used to analytically construct time-elongation profiles which are then
fitted with the two methods. It is found that higher angles and velocities give
rise to greater error in both methods, reaching errors in the direction of
propagation of up to 15 deg and 30 deg for the F\Phi and HM fitting methods,
respectively. This is due to the physical accelerations of the CMEs being
interpreted as geometrical accelerations by the fitting methods. Because of the
geometrical definition of the HM fitting method, it is affected by the
acceleration more greatly than the F\Phi fitting method. Overall, we find that
both techniques overestimate the initial (and final) velocity and direction for
fast CMEs propagating beyond 90 deg from the Sun-spacecraft line, meaning that
arrival times at 1 AU would be predicted early (by up to 12 hours). We also
find that the direction and arrival time of a wide and decelerating CME can be
better reproduced by the F\Phi due to the cancellation of two errors:
neglecting the CME width and neglecting the CME deceleration. Overall, the
inaccuracies of the two fitting methods are expected to play an important role
in the prediction of CME hit and arrival times as we head towards solar maximum
and the STEREO spacecraft further move behind the Sun.
