  The NASA STEREO mission opened up the possibility to forecast the arrival
times, speeds and directions of solar transients from outside the Sun-Earth
line. In particular, we are interested in predicting potentially geo-effective
Interplanetary Coronal Mass Ejections (ICMEs) from observations of density
structures at large observation angles from the Sun (with the STEREO
Heliospheric Imager instrument). We contribute to this endeavor by deriving
analytical formulas concerning a geometric correction for the ICME speed and
arrival time for the technique introduced by Davies et al. (2012, ApJ, in
press) called Self-Similar Expansion Fitting (SSEF). This model assumes that a
circle propagates outward, along a plane specified by a position angle (e.g.
the ecliptic), with constant angular half width (lambda). This is an extension
to earlier, more simple models: Fixed-Phi-Fitting (lambda = 0 degree) and
Harmonic Mean Fitting (lambda = 90 degree). This approach has the advantage
that it is possible to assess clearly, in contrast to previous models, if a
particular location in the heliosphere, such as a planet or spacecraft, might
be expected to be hit by the ICME front. Our correction formulas are especially
significant for glancing hits, where small differences in the direction greatly
influence the expected speeds (up to 100-200 km/s) and arrival times (up to two
days later than the apex). For very wide ICMEs (2 lambda > 120 degree), the
geometric correction becomes very similar to the one derived by M\"ostl et al.
(2011, ApJ, 741, id. 34) for the Harmonic Mean model. These analytic
expressions can also be used for empirical or analytical models to predict the
1 AU arrival time of an ICME by correcting for effects of hits by the flank
rather than the apex, if the width and direction of the ICME in a plane are
known and a circular geometry of the ICME front is assumed.
