# NavList:

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

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Re: Measuring (and calculating) Dip
From: Marcel Tschudin
Date: 2013 Feb 27, 23:39 +0200
Brad, regarding your following explanation for the origin of the value 0.02977 for calculating the dip

I have seen

dip = arccos ( (R/(1-k)) / ( h + R/(1-k)) )
where R is the radius of the earth
k is the refraction factor (?)
h is the height of eye
But in this equation, we are left to guess at k, nominally assigned a value of 0.13.  In doing so, the equation agrees within seconds to the 0.02977 result.

I forgot before to put the corresponding k=0.13 value in relation to some other commonly used dip values:

Bowditch (and I think the same is also in the N.A.) provides the formula Dip=1.76 moa * SQRT(H in m); this corresponds to k=1.6.

Calculating refraction by ray tracing with the standard atmosphere and standard condition (10C, 1010hPa) one obtains a dip which corresponds to k=0.17

Replacing in the standard atmosphere the lapse rate in the troposphere with the dry adiabatic (10K/km) or the wet adiabatic (5K/km) ones result correspondingly in k=0.15 (dry) and k=0.18 (wet).

I also did come across a Web-page (in German) which mentions k=0.13 (or rather 1/8) but adds also that during the night with covered sky k may be 0.2 and during nights with clear sky may reach up to 0.3.

I am still in the process of analysing my measurements of refraction plus dip during sunsets (sun below about 4 deg above horizon) and am still trying to find useful correlations which will improve the results. I am therefore not yet in a position to propose a best estimate for the dip. Present (preliminary) results indicate that with the parameters which were derived from the standard atmosphere the calculated refraction plus dip agrees reasonably with the mean values (actually rather the medians or even better the modes) of the heavily scattering  measurements.

Marcel

P.S: I will answer separately your last contribution which only just arrived.
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