  We perform four numerical magnetohydrodynamic simulations in 2.5 dimensions
(2.5D) of fast Coronal Mass Ejections (CMEs) and their associated shock fronts
between 10Rs and 300Rs. We investigate the relative change in the shock
standoff distance, Sd, as a fraction of the CME radial half-width, Dob (i.e.
Sd/Dob). Previous hydrodynamic studies have related the shock standoff distance
for Earths magnetosphere to the density compression ratio (DR,Ru/Rd) measured
across the bow shock (Spreiter, Summers and Alksne 1966). The DR coefficient,
kdr, which is the proportionality constant between the relative standoff
distance (Sd/Dob) and the compression ratio, was semi-empirically estimated as
1.1. For CMEs, we show that this value varies linearly as a function of
heliocentric distance and changes significantly for different radii of
curvature of the CMEs leading edge. We find that a value of 0.8+-0.1 is more
appropriate for small heliocentric distances (<30Rs) which corresponds to the
spherical geometry of a magnetosphere presented by Seiff (1962). As the CME
propagates its cross section becomes more oblate and the kdr value increases
linearly with heliocentric distance, such that kdr= 1.1 is most appropriate at
a heliocentric distance of about 80Rs. For terrestrial distances (215Rs) we
estimate kdr= 1.8+-0.3, which also indicates that the CME cross-sectional
structure is generally more oblate than that of Earths magnetosphere. These
alterations to the proportionality coefficients may serve to improve
investigations into the estimates of the magnetic field in the corona upstream
of a CME as well as the aspect ratio of CMEs as measured in situ.
