# NavList:

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

**Re: Stop and smell the equations**

**From:**Bruce J. Pennino

**Date:**2013 Apr 9, 19:56 -0400

Bruce

----- Original Message -----From:Frank ReedSent:Monday, April 08, 2013 10:42 PMSubject:[NavList] Re: Stop and smell the equations

Bruce, you wrote:

"My, my...bad to worse...seems a bit......harsh."I do apologize if you took that personally. It was absolutely not directed at you. I was referring to Brad's recent posts which have been bouncing rapidly from one equation to another without stopping for even a moment to understand what the equation means. It has indeed gone from "bad" to "worse".

You also wrote:

"By the way, instead of using a "tangent offset" calculation method for a dip equation"What do you mean by a 'tangent offset' calculation??

And:

"I redid the geometric dip more correctly using right triangle geometry and trig, based solely on the equivalent radius of the earth."Yes. That's right. That's exactly how it works. You can do any of the various calculations for things like dip, dip short, angles to objects at different distances, distance to the horizon, angular height of an object beyond the horizon, and so on, by doing PURE Euclidean geometry problems, solved by simple trigonometry and often greatly simplified and reduced by small angle series expansions, etc., and THEN, to replace the pure geometry and bring the physics of refraction into the problem, you can just replace the radius of the Earth by the effective radius of the Earth given by R/(1-k) and all of the results will be correct for cases where the refractive "rotation" k is given. In the real world, this rotation has to be measured. Its average value has been well-established for nearly 200 years. But once it is given, either the average or a unique weather-specific value, the other equations follow without any further work. This only works under the assumption that the refraction does not vary much with geography across the region under observation. And even that condition may easily be violated in real world cases.

You continued:

"This way, geometric dip K was calculated to be 1.06 as Frank and others have mentioned. Due to refraction correction and experience, the adopted value is 0.971, or so."That's right. Note that the third digit beyond the decimal point in 0.971 is probably not significant. You might as well use 0.97. Also, bear in mind, as Marcel also noted, that you need to be very careful about which "k" you mean. It's always a good idea to specify what k means in every case.

You also wrote:

" It appears that we are trying to refine a small percentage of the total dip equation....roughly 7% or so. "May I ask, where are you getting that "7%" from? It is quite possible in the case of a temperature inversion that k (in R/(1-k)) can be 0.5 or 0.7 or quite a range of other values. These are relatively uncommon situations but not "rare". Don't take this to imply that the dip equation is "broken". The idea that there is something "wrong" with the standard dip equation and that it needs to be "fixed" --if, in fact, anyone is still under that impression-- is misguided. The value of 0.97 as the factor for sqrt(h) (h in feet) is a well-established average choice. Common daily variations in the range 0.90 to 1.00 are not at all unusual, and much larger variations in dip do sometimes occur.

-FER

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