# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Equation for dip?**

**From:**Frank Reed CT

**Date:**2006 Oct 1, 01:13 EDT

Jim Van Zandt wrote: " I wonder whether that's because of the different wavelength, or different typical heights (so different temperature and pressure profiles), or what?" It's the index of refraction in air at visible wavelengths and the rate at which it changes with atmospheric density. The rate of change of atmospheric density, and therefore index of refraction, depends on the lapse rate (the rate of temperature variation) in the lower atmosphere. If the air gets colder with altitude much more rapidly than normal, the air density can actually be constant with height. Under those circumstances, the air does not refract at all. The dip equation then is exactly the same as the equation you would get from a straight geometric calculation. Or in other words, the effective radius of the Earth is the same as the true physical radius. I should say, though, that this is a limiting case. When the air has that temperature profile and constant density with height, it is extremely unstable and convection will set it in almost immediately and bring the lapse rate closer to the normal rate. At the other extreme, if the air gets warmer with height at a rather high rate, the effective radius of the Earth becomes infinite --as if the Earth were flat-- and the dip is exactly zero at all heights. Under these circumstances, the horizon is infinitely far away and you can see across an ocean. In the real world, scattering and absorption in the atmosphere makes distant objects disappear in a haze before the horizon but the limiting distance may be ten times farther away than a "normal" calculation would predict. And, yes, if the lapse rate gets even steeper, the effective radius becomes negative and the sea would appear to climb up into the sky above the true horizon. Generally, the normal, daily variability of the lapse rate is equivalent to a much more moderate variability in the effective radius of the Earth; one day 15%, another day 17%... You can literally imagine the Earth's surface flexing up and down with the weather to picture this. It works for any surface refraction phenomena including dip, range of visibility, distance by height above the horizon, etc. All surface (terrestrial) refraction phenomena are affected by this in the same way. -FER 42.0N 87.7W, or 41.4N 72.1W. www.HistoricalAtlas.com/lunars --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---