I find this website very helpful for visualizing the changes in daylight over 
time and latitude.

Daylight Hours Explorer
http://astro.unl.edu/classaction/animations/coordsmotion/daylighthoursexplorer.html


> On Feb 3, 2015, at 3:36 PM, sundial-requ...@uni-koeln.de wrote:
> 
> OK, I would also like to take a turn and ask a question to the mathematically 
> inclined:
> 
> I have been trying to figure out how to plot the duration of daylight over 
> the course of the year as a function of latitude. (I would generate a curve 
> for each latitude I am interested in.)  
> 
> I believe the result should be a sine curve which looks comparatively flat at 
> the equator, growing increasingly steeper until the polar circle, where it 
> would turn into a binary step curve and the six month day turns to six month 
> night -- leaving aside physical effects like refraction.  I am particularly 
> interested in the slope of the curve around the equinoxes at northern 
> latitudes, when the transition from long summer days to short winter days is 
> quite abrupt.     
> 
> Jack Aubert  

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