# NavList:

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

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Re: Table 8, Bowditch
From: Ark Shvetsky
Date: 2009 Jan 13, 18:53 -0800

```Frank, you gave me� very clear, down-to-the-Earth� answers.� I thank you very much!

----- Original Message ----
From: "frankreed@HistoricalAtlas.com"
To: NavList@fer3.com
Sent: Tuesday, January 13, 2009 6:07:38 PM
Subject: [NavList 7042] Re: Table 8, Bowditch

"Just wants to make it clear for myself :>: to calculate a distance to the
visible horizon I need to use statute miles, not nautical.� Is this a correct
statement?"

No, I was just talking about a mistake that people sometimes make that causes
confusion because it seems to yield the table values without any refraction
correction. But not to worry: everything is nautical miles in navigation
calculations.

And:
"Also, just curious: radio waves and light wave are electromagnetic waves
which are differ in frequency.� Therefore, it means the refraction-wise high
frequency signal is refracted more.� Is it logarithmic or just a linear
correlation for refraction rate between low and high frequency waves?"

The variation of refraction with frequency is called a "dipersion relation."
There are no simple rules for such things. In fact red light, which has a
longer wavelength, bends less than blue light which is opposite the apparent
rule for radio versus visible light.

"you also mentioned a temperature gradient in the low atmosphere as a factor
which may effect visible horizon's distance calc by 15-20%� Is it included in
the Table 8?.� If not, how to apply this correction factor to the
calculation?� Another table exist, I presume?"

First, I said this wrong. It's maybe 10-20% (in many cases) of the correction
factor which is itself a number around 0.15 so the actual variation in the
distance to the horizon is much smaller: a couple of percent under common
conditions. But under somewhat more extreme meteorological conditions, it can
be much greater. In fact, if the temperature changes at just the right rate,
light rays will travel parallel to the Earth's surface, and, therefore, the
horizon is technically at infinite distance (visually it just vanishes in a
distant "fog"), and you could expect to see vessels and other objects dozens
of times farther away than normal. So how do we correct for this? The
suprising answer is that we can't. First of all, we can't measure the actual
temperature profile of the air between us and the horizon. And equally
important, this is just one type of variation in the refraction. In the real
world, there can be much more complex variations in
atmospheric conditions resulting in mirages and so on. But even if we can't
correct for it, there is still a point to all of this. When you look at these
tables for distance to horizon, dip, and dip short, etc., you need to bear in
mind that they apply to mean conditions. In practice, dip and distance to the
horizon are somewhat variable.

-FER

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