You can calculate this using some basic trigonometry.
Here is a very nice and well documented explanation of how to calculate the length of day and the duration of twilight for any latitude and for any day of year.
You can also read this discussion on http://mathforum.org which mention an article in Ecological Modeling, volume 80 (1995) pp. 87-95, called "A Model Comparison for Daylength as a Function of Latitude and Day of the Year."
This article presented a model that apparently does a very good job
of estimating the daylight - the error is less than one minute within
40 degrees of the equator, and less than seven minutes within 60
degrees and usually within two minutes for these latitudes.
I figured that if other people were having trouble finding this
information, too, maybe it would be worth saving them some time by
letting you know what I found. So, here's the model:
D = daylength
L = latitude
J = day of the year
P = asin(.39795*cos(.2163108 + 2*atan(.9671396*tan(.00860(J-186)))))
D = 24 - (24/pi)*acos( (sin(0.8333*pi/180) + sin(L*pi/180)*sin(P)) / (cos(L*pi/180)*cos(P)) )
Use a radian mode here, but latitude should be entered in degrees.
Note, that the day of year J probably does not start with the January 1st, but with the day of the winter solstice in the first year a four years cycle.
Using this, you should be able to generate the day/night curves you need so it almost matches the reality.