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Old 19th Jul 2010, 20:39
  #5 (permalink)  
selfin
 
Join Date: Apr 2004
Location: Tomsk, Russia
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For a spherical earth, try:

acos[R/(R+z)] * 60/15 = minutes offset.

R is the spherical planet's radius, z is the aircraft altitude above the surface. Remember to use the same units. The sunrise time at altitude leads the time at the surface by the value of the offset and lags behind the surface time value during sunset.

There is obviously no account of refraction: normally at the surface 0.833° is used (3"20') but I have no idea how this should be varied with altitude. Secondly, the offset should be multiplied by the cosine of the subsolar point latitude. The worst case scenario only requires the offset to be reduced by about 8% - corresponding to the solstices.

Here's a plot of the above. In the lower plot the abscissa/ordinate axes are the same as the upper one - forgot to add the labels.

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