You might try a meteorological journal like MWR (Monthly Weather Review, although the title is now quite anachronistic -- this is the journal I'd recommend for your work) or JAS (Journal of Atmospheric Science) for this sort of thing (these are both first-tier journals in our field), as we (meteorologists) care very much about the accuracy and speed of great circle distance calculations for weather/climate forecast models and data assimilation. The American Meteorological Society website has a set of guidelines for submission, so just follow those and submit. You automatically have copyright, of course, but this isn't a patentable sort of thing -- it sounds like a short journal article or note to me. You don't need any kind of qualifications to submit -- if the paper is good and appropriate for the journal, it will get published. It will not be free; however, if you refrain from using color, the page charges won't be too bad.
Dr. William F. Campbell
Marine Meteorology Division
Data Assimilation Section
Naval Research Laboratory
Monterey, CA