 # NavList:

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

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Re: formula for refraction
From: Bill B
Date: 2007 Mar 21, 21:54 -0400

```Frank wrote:

> The formulas given in various sources on the pattern of
> Ro = 0d.0167/tan(H + 7.32/(H + 4.32))
> are simply numerical "fittings". They're not "derived" from underlying theory.
> In my code, I use two different equations, one for altitudes above 15 degrees,
> one for lower altitudes. At higher altitudes, R = 57"/tan(H) is excellent. If
> you adjust the parameters in the other formula (above), you can get better
> results at lower altitudes. From the perspective of accuracy and technical
> quality, this is NOT a better solution than inputting the whole table, but it
> certainly involves less typing. :-)

R = 57"/tan(H

Do we use the decimal degree equivalent of 57" (0.0158333)?

If so, is the refraction (not correctly signed) then given in decimal
degrees?

If so, multiply refraction in decimal degrees by 60, and then column H is
decimal minutes.  Or use 0.95 instead of 0.0158333 to get decimal minutes
directly.

At this point I have elevation (H) in column G as degrees, and refraction
(R) as positive minutes in column H.

For example:

G   H
40  1.13
41  1.09

So far so good?

Now I type the elevation (H) into cell B2, say 40.5d.
In cell C2 I copy and paste your instructions:

=VLOOKUP(INT(B2),G10:H100,1)*(1-(B2-INT(B2)))+VLOOKUP(INT(B2)+1,G10:H100,1)*
(B2-INT(B2))

Here is where I have gone wrong.  Excel is returning the same value in C2 as
was entered in B2--40.5.

Any hints or tips?

Thanks, and welcome back from Mac-OS Land.

Bill

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