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From: Bill (no email)
Date: Wed Jan 11 2006 - 02:02:31 EST
Frank wrote:
> "I have done three trial runs with the new values, and they seem to approach
> reality with the average of mean refraction values derived from the two
> methods above, a least when height of eye is 0."
>
> Can you elaborate on this 'reality' you speak of? <g> Seriously, how are you
> assessing the results.
First a disclaimer--I do not claim to be the sharpest crayon in the box.
To calculate the angle that "should be" observed in mean conditions:
Height of object in feet - hidden part of object with no atmosphere + lift
due to refraction. This is converted to nautical miles. (Divided by 6076.11)
Then divided by distance in nautical miles = tangent of theoretical observed
angle. I am treating it as a right triangle for this round, as the
difference between that and an oblique triangle is insignificant--as you
pointed out.
For lift due to refraction, I am averaging the lift in feet from the angle
you suggested--0.15 minutes per minute--and lift from the web page you
referenced. I had converted the meters scale to feet-per-nautical mile:
Nautical miles^2 * .287 = lift in feet.
For hidden portion, I used 21600/2*pi as earth's radius (R). Angle A (from
center of earth) was distance in nautical miles AKA arcminutes along the
surface. Hidden portion in nautical miles calculated as (R / cos A) - R.
Then converted to feet (*6076.11).
I recognize I am paining with a broad brush. I understand my assumed values
for R, 6076.11, etc. change depending on position on the earth and the
latest research. Also that I am using a mean value for refraction. Hence I
am playing with mean values (as I understand them) of "reality" at this
juncture. <G>
Of concern to me is my use of the relationships in the Bowditch equation to
derive new constants. Is the equation valid? Does H-h hold up?
Of greater interest is that the Bowditch "system" seems to be internally
consistent. To follow up on your use of a 0.15 constant (R/(1-.15) for
calculating dip, short dip etc., one might question the entire system. If
dip is drop of the horizon due to earth's curvature, plus lift from
refraction, then dip is overstated given current values of lift due to mean
refraction. We use those dip values in cel nav with current values of
refraction for non-terrestial objects. Huh?
Bill
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