It was shown by G. D. Thayer and J. J. Freeman that corrections to refraction-induced errors can be expressed in terms of error functions for propagation in an exponential model atmosphere. Using Freeman's equations as an example, we replace the error functions by their asymptotic expressions, thereby giving closed form equations. To extend the usefulness of these functions for short ranges and small elevation angles, an empirical adjustment is made.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.