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-----Original Message-----
> Jim wrote:
>> In another section he shows how to derive the constants 0.0002439 and
>> 0.7409.  Note that 0.7409 is not 0.7349, the constant used in the current
>> 2002 Bowditch.
>
> From Bill:
> Ah, the .7349 constant has been driving me nuts.
> Horizon is 1.169 (SQRT height of eye, ft).
> Geographical range, with height of eye = 0 is 1.17 * SQRT height
> of object.
> Note the difference between 1.169 and 1.17 is most likely because
> the object
> has to be a smidge over the horizon to be seen.
> Both the above are flip sides of the same coin.
> In the table 15 formula if I set the the observed angle, corrected for IC
> and dip to 0, and height of eye to 0, I get
> D = SQRT (H/.7349) = SQRT (H * 1.36184) = SQRT H * SQRT 1.36184 = 1.167*
> SQRT H
> Beginning to look familiar?  By why the difference between 1.167 and 1.169
> or 1.17?
> Using .7409 and running through the above exercise, it becomes
> 1.162 * SQRT H
> It is puzzling to me.

Bill, I don't know if this might help, because I am not at all confident in
my ability to read navigation literature that is this technical.

Guier was interested in improving the precision of the method.  Among other
things, he tried to find a better terrestrial refraction constant that could
be applied across the range covered by his extended table.  He assumed that
rR/r0 is approximated by 1.192, where rR is the refracted equivalent of the
earth's radius, and r0 is the earth's radius (he used r0 = 3,440.0 NM).
Bowditch's original equation used rR/r0 = 1.18.  This refinement resulted in
a correction of about 0.5% of the range, so the differences are more
significant for high objects and small angle (large range).  The distance to
the horizon is commonly given as 1.17 * sqrt(height of eye in feet), as you
noted.  The differences, as I read it, has to do with how he calculated the
1.192 constant, based on his method for deriving the observer's dip of
horizon prior to deriving that approximation for rR/r0.

Having obtained rR/r0 =(approx) 1.192, he then reports the two constants
0.0002439 and 0.7409.  I cannot follow the mathematics well enough to
explain how he derived either of them, and I have no explanation at all for
the variance between that constant and the 0.7349 that we see in Bowditch
today.

I see now that BOTH of his constants differ from today's Bowditch:
Guier: 0.0002439 and 0.7409.
Bowditch: 0.0002419 and 0.7349.
Although it must be noted that the equations are not syntaxed precisely the
same.

These differences remain a mystery to me, but I have to make supper for the
family now.

Jim

   

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