# NavList:

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

Message:αβγ
Message:abc
 Add Images & Files Posting Code: Name: Email:
Refraction
From: Dave Walden
Date: 2008 Jul 3, 16:18 -0700
Refraction
Attached is a small spreadsheet that calculates the K coefficent for the horizontal mulitlayer atmosphere and the A and B coefficents for spherical layer atmosphere.  (Errors may remain.  Please comment.)  They are functions of pressure, temperature and wavelength.  Two sets of conditions can be caluclated for easy comparisons.  Those included are for the Nautical Almanac conditions and a more conventional set to conditions: 760mb, 0 deg C, lamda .54 microns.   The K =60.4 sec, should look familiar.  The Naut Alm STP yields 58.2, also familiar.  Neither is right.  They're just different.  Starting with either and adjusting to conditions for a specific observation will yield the same answer.
The formulas can be found in Spherical Astronomy by Green.  This is the "successor" to Smart's work.  Green was coauthor with Smart on later editions and finally wrote his own.  (To my way of thinking, it's better.)
Also attached is a plot of errors of Bennett and simpler formulas (minutes refrac vs degrees alt).  There is indeed, nothing magic about Bennett.  It get 34 min at 0 deg in case you've forgotten, but the added complication to do so only makes things worse at higher altitudes.  (the curve labeled 1term is the planar atmosphere model with just K. It's better than Bennet at all angles above 13 degrees.  The hoen-walden is a LaPlace formula with A and B. Its better at all angles above 7 degrees.  (The 1 and 2 term formulas blow up at zero, so just don't use them for very small angles.)

The link below is supposed to take you to page 41 of Modern Astrometry by Jean Kovalevsky which shows graphically the effect of wavelength on refraction

***********************************************************************************
Kent, you wrote:
"The factor 60,35” has been provided to me from the Observatory in Stockholm
to be used with the true zenith altitudes for altitudes above approx. 10
degrees. The factor is taken from modern English litterature."
What color light? It's not often mentioned explicitly that this factor
applies only for one specific frequency in the visible spectrum. That's one
reason why two people can quote factors differing by an arcsecond and still
be technically correct. It's also why we shouldn't worry too much about the
tenths and hundredths of an arcsecond. And it's a big reason why we
shouldn't shoot lunars when the objects are below about ten degrees: the
stars and the limbs of the Sun and Moon are stretched out into colorful
bands at very low altitudes. Incidentally, I use 58" usually.
And:
"Yes, this is correct. For altitudes below 20 degrees I use the formula
defined by Smart."
Since you're modeling historical methods, you could just input the whole
refraction table as printed. Then the software would interpolate between
values much as a 19th century navigator would have done on paper. This
approach bypasses all this chatter about various formulae for different
altitudes. It's also a reasonable approach for a modern analysis. Sometimes
people doing these calculations obsess over the "Bennett" formula. This is
because we carry around "baggage" from the calculator era and the early
years of programming small computers. There's no real advantage to a short
formula today (except saving a few keystrokes).

--~--~---------~--~----~------------~-------~--~----~
To post, email NavList@fer3.com
To unsubscribe, email NavList-unsubscribe@fer3.com
-~----------~----~----~----~------~----~------~--~---

Browse Files

Drop Files

### Join NavList

 Name: (please, no nicknames or handles) Email:
 Do you want to receive all group messages by email? Yes No
You can also join by posting. Your first on-topic post automatically makes you a member.

### Posting Code

Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
 Email:

### Email Settings

 Posting Code:

### Custom Index

 Subject: Author: Start date: (yyyymm dd) End date: (yyyymm dd)