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    Re: Refraction -- A general formula for all heights and altitudes
    From: Frank Reed CT
    Date: 2005 Aug 25, 16:21 EDT

    I neglected to mention that Alt is input in  degrees and Ht is in meters. Alt
    should be between -3 and 90. Ht should be  between 0 and 8000m -- outside
    this range is ok but with lower  accuracy.
    'Alt is the  angular  height (corrected for dip). Ht is the observer's height
    above sea   level.
    IF Alt < 0 THEN
    'use new below zero degrees altitude   formula:
    refx = EXP(3.537 - .369 * Alt + .051 * Alt * Alt)
    ELSEIF Alt  <  15 THEN
    'use standard low altitude refraction formula  (Bennett):
    refx =  .998 / TAN((Alt + 7.31 / (Alt + 4.4)) /  kk)
    'use standard high  altitude refraction:
    refx = .972 /  TAN(Alt / kk)
    END IF
    'refx as  calculated so far is the sea level  refraction at standard
    temperature  and
    'pressure of 10 deg C and  1010 millibars. The result is in minutes of  arc.
    'Now adjust for  non-standard tempreature and pressure.
    'Temp and  Press are sea level  temperature in deg C and pressure in mbar:
    refx = refx *  (Press / 1010)  * (283.15 / (273.15 + Temp))
    'Now scale for  height above sea  level:
    'Primary scaling with height above sea level:
    refx  = refx *  EXP(-ht / (11278 - ht / 13))
    'A correction in scaling for very low   angular altitudes, proportional to
    observer altitude:
    refx = refx - (ht  /  10000) * EXP(-Alt / 14)
    'refx is in minutes of   arc.
    42.0N 87.7W, or 41.4N  72.1W.

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