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

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Re: Refraction near the Horizon ? Observation vs. Calculation
From: Frank Reed
Date: 2013 Apr 11, 09:50 -0700

"Additionally, the equation Dip,min = 3438*sqrt(2*HoE/R) was offered. In this equation, R was not defined and was assumed to be Rgeom. Upon further contemplation, it has become evident that R is meant to be Rrefr."

Astonishing. Nope. You are still confused. This equation was not "offered" as anything except a step in a derivation (and I said as much in a follow-up directed to you, as well). It is really WEIRD that you became obsessed over it. If there's anyone following along who has not seen the original context (and still cares in the slightest), here is the full message:
http://fer3.com/arc/m2.aspx/Refraction-near-Horizon-Observation-vs-Calculation-FrankReed-apr-2013-g23362.
And here is the extract with that equation as an intermediate step:
[after a couple of opening paragraphs]
"And finally:
d = sqrt(2*h/R).
This version of the equation applies for any units, and its result is an angle as a pure ratio. But if we want the angle in minutes of arc, we have to multiply by 3438:
d = 3438'*sqrt(2*h/R).
The value of the Earth's true radius is a fixed number. If h is in feet, then we should express the radius in feet. That's about 20,909,000 so now
d = 3438'*sqrt(2*h/20909000).
Pull the constants out of the square root and you get
d = 1.06'*sqrt(h), when h is in feet.
This geometric results was worked out centuries ago, but when dip was measured, the results were always smaller. " [etc.]

And you can continue reading, to find out how the geometric dip has to be modified to better approximate the true dip, in that full message.

It's just astounding to me, Brad, that you could be so wildly confused over the original meaning of that equation in that context. It's surreal.

As long as we're at it, "pi" is not "pi()" unless you live inside a spreadsheet. And quoting the radius of the Earth to two significant figures when you give the refraction constant to three (and pi to nine digits) is obviously bad.

"Using a value like 3438, without showing that it was approximately 180/pi(), is a Magic Number. When writing software, we often create a variable to avoid Magic Numbers. For example, we could state MinutesConversion = 180/pi()*60. [...] When Magic Numbers, as opposed to variables, appear in code, they often lead to programming errors."

Oh do "we"? Thank you so much. I shall now re-write the thousands and thousands of lines of code that I have generated for celestial mechanics, positional astronomy, and celestial navigation to include this super-duper constant! Oh, wait. I've been doing that since 1979. It's standard practice. But you see, Brad, this isn't a programming class. That post was intended to be comprehensible to anyone with a strong high school math background --not for programming geeks. I have no intention of tailoring my posts to satisfy your "unique" needs. But if you have a QUESTION about anything, feel free to ask.

Bradley, after posting yet another confused pseudo-mathematical ramble, you wrote:
"That said, of late you have demonstrated what some may consider to be rather coarse behavior, to me and to others. Rather than presenting you with a list of these obvious transgressions, I would urge you to think for a moment, when you are rude to folks, after a while, they become rude in return. When you say nasty things about someone's work product, they will eventually begin to return the favor, and say nasty things about your work product. You probably didn't mean for it to come across that way, but it did."

Brad, I look forward to your next posts on the mathematical aspects of the subject, if any, but there's no free ride here. If you post nonsense, you can expect to have it called out, by me or someone else. I trust that this will be the last of your adolescent rants about my "transgressions" (oh no, I have transgressed against him!). And I trust that your attempts at tit-for-tat assaults on other people's "work product", as you so quaintly put it, are also now at an end.

But we'll see...

-FER

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