  Accurately predicting the arrival of coronal mass ejections (CMEs) at the
Earth based on remote images is of critical significance in the study of space
weather. In this paper, we make a statistical study of 21 Earth directed CMEs,
exploring in particular the relationship between CME initial speeds and transit
times. The initial speed of a CME is obtained by fitting the CME with the
Graduated Cylindrical Shell model and is thus free of projection effects. We
then use the drag force model to fit results of the transit time versus the
initial speed. By adopting different drag regimes, i.e., the viscous,
aerodynamics, and hybrid regimes, we get similar results, with the least mean
estimation error of the hybrid model of 12.9 hours. CMEs with a propagation
angle (the angle between the propagation direction and the Sun-Earth line)
larger than its half angular width arrive at the Earth with an angular
deviation caused by factors other than the radial solar wind drag. The drag
force model cannot be well applied to such events. If we exclude these events
in the sample, the prediction accuracy can be improved, i.e., the estimation
error reduces to 6.8 hours. This work suggests that it is viable to predict the
arrival time of CMEs at the Earth based on the initial parameters with a fairly
good accuracy. Thus, it provides a method of space weather forecast of 1--5
days following the occurrence of CMEs.
