Constellation rise times versus hour of darkness .....etc

I've been waiting to observe M27 in Cygnus, and a thought ocurred to me
recently when I noticed that it is quite high in the sky when it gets dark -
about the same altitude that I remember from last October when it 'got dark'
then (i.e. earlier in the evening). I know that the altitude of Cygus at a
given local time each night will vary roughly linearly with time of year
(day number), but my thought was this: if we were to plot the altitude (or
rise time) of a given object versus the time at which the sky brightness
falls to a given magnitude (i.e. some indicator of the time that 'darkness'
falls), what would it look like? Would there be stationary points, or even
retrogade behaviour? And how would this curve vary with the observer's
lattitude?

Anyone know of websites with relevant equations / graphs? Another topic that
interests me is the relationship between the length of twilight and
latittude / time of year, and also the shape of the curve for rate of change
of day length versus time of year (i.e when does day length change most
quickly etc). Also rate of change of length of twilight........and how is
this defined? .........

Just wondering :-)

Alan