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    Re: dip, dip short, distance off with buildings, etc.
    From: Bill B
    Date: 2006 Jan 11, 02:02 -0500

    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?   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
    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?

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