The sine curve of life at 48° N

Warning: serious dorkiness ahead.

It occurred to me a couple years ago that the pattern of daylight hours was a sine curve, which is entirely unsurprisingly when you figure the circles involved. But I really like the mental reference of seeing where I am on the curve throughout the year.

As I was laying in bed a couple nights ago, watching the inky blue sky slowly darken and marveling at how long the days were a full month out from the solstice, I found myself thinking about the curve.

So I decided to graph it. As you do when you’re nerdy enough to have a favorite sunrise/sunset calendar website.

sine daylight

It turns out daylight at 48° north is pretty close to 4 * sine(day) + 12, where days count from the spring equinox. Adjust that 4 based on the difference between your longest/shortest day length the 12 hours at the equinoxes and you could have your very own sine curve…

I was surprised to see how much the actual daylight curve is kinder than expected slipping into the darkest days. And how did I not know that the solstices were not quite symmetrical – winter is only 3.65 hours shorter than at the equinox here while the summer solstice is 4.07 hours longer?

I was also too lazy to adjust for the fact that there are 5 more days in a year than degrees in a circle, thus the weird gap.

Fascinating, no? No? Alright, then. Carry on with your weekend plans not involving recreational spreadsheets.