Just some idle speculation:
If we assume that CMEs are directed directly away from the centre of the
sun, which seems reasonable, and we know the initial diameter of the cloud,
its rate of expansion and the velocity away from the sun, it is a simple
matter to calculate how far the edge of the cloud will be from the Earth,
when it passes us.
The initial size might be a problem, but if clouds grow to many times that
size by the time they reach us, we can ignore it. The main question is the
rate of expansion and the velocity of the cloud. This information can
probably be gleaned from previous CMEs. I seem to recall that it takes 3 or
4 days to reach us, which gives a velocity of about 1 to 1.3 million mph and
at a guess we may assume the same rate of expansion.
To miss the Earth by 7.5 million miles, the angle away from the sun-earth
line is approx arctan((93+7.5)/93), i.e. about 47 degrees. As viewed from
the Earth, the CME must start from outside a circle of about .73 of the
visible diameter to miss the Earth by the required amount.
Or to put it another way the probabability of any arbitrary CME missing the
Earth by that amount is approx 80%.
A more reliable method might be to look through the statistics available on
the Internet from places like:
73 John, G4CNN
Send a cool gift with your E-Card