# NavList:

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

**Re: Refraction for beginners**

**From:**Paul Hirose

**Date:**2004 Jul 11, 13:36 -0700

For bubble observations I would omit refraction corrections for nonstandard pressure and temperature, and just apply a correction for altitude above sea level (if significant). For that, assume a standard atmosphere. Putting "standard atmosphere" in a search engine will reveal many online calculators to give you the air density if altitude is known. This one is convenient because you can select "sigma" for the density units. Sigma is density relative to sea level. http://www.digitaldutch.com/atmoscalc/ If you input 5000 feet for altitude, you'll see that sigma = .86, so the refraction correction would be 86% of the value listed in the Nautical Almanac. That assumes the temperature vs. altitude relationship is standard. According to the calculator, standard temperature at 5000 feet is 41 F. But suppose the actual temperature is 90 F. The increased temperature reduces the air density (and refraction), the correction factor being equal to the ratio of the absolute temperatures. In my example they are 41 F and 90 F, so the temperature correction factor is (460 + 41) / (460 + 90) = .91. (The number 460 converts from Fahrenheit to degrees above absolute zero.) Finally, suppose the barometric pressure is 29.7 inches Hg instead of the standard 29.9. To correct for that, the multiplier is 29.7 / 29.9 = .99. To apply all the corrections, multiply the Almanac refraction by .86 * .91 * .99, for an overall correction factor of .77. If the tabulated refraction is 6', the adjusted refraction becomes 4.6'. If we had neglected the corrections for nonstandard temperature and pressure, it would be 5.2'. That's not much different, even though my example had large deviations from standard conditions and the corrections were in the same direction. If you want to get anal-retentive, this person has a site with formulas for determining air density in several different ways: http://www.wahiduddin.net/calc/density_altitude.htm It has links to authoritative references for such things as exactly how the "raw" station pressure is converted to barometric pressure corrected to sea level, or altimeter setting.