Friday, January 28, 2011

Days Growing Longer Faster

At the winter solstice, the shortest day of the year in the northern hemisphere, night loses the upper hand and the days begin to get longer and longer. At first slowly, imperceptibly, then faster and faster until we reach the middle of spring when each day is three minutes longer than the day previous.

I found this great graph that illustrates the rate of change.

On December 21, the winter solstice, the daily variation is nearly zero, which means that the length of daylight on that day is pretty much the same as the day before and the day after. 

Now take a look at today, the tail end of January. Each day is more than two minutes longer than the day previous. Tomorrow's daylight is going to be 2 minutes and 23 seconds longer than today's. 

During the entire month of March, each day will be more than three minutes longer than the day previous. That's more than an hour and a half gain in daylight over the month. 

You can see that the curve also flatten in March, and at the spring equinox the rate of change begins to slow until we pause at the summer equinox toward the end of June. Just like at the winter equinox, the rate of change is essentially zero, and the difference in daylight between the days is measured in seconds.

At this time the days start getting shorter and shorter, the rate of change accelerating and reaching a peak of around three minutes shorter per day at the end of September, at the Autumnal equinox. 

But after that, the rate of change slows and slows as we approach the winter solstice when the rate of change again becomes zero, when we again pause before reversing...and the whole thing starts over again. 

I just wanted to share this. 


  1. Your posts are always interesting and fun to read, Jack, but since you went to a smaller font they're hard on my old eyes. Could you bump it up a few points, please? Thanks.

  2. Hey Bruce,

    I haven't changed the font size for the blog. Try pressing "ctrl+" (Ctrl key and "+" key simultaneously) to increase the font display size in your browser. Likewise, Ctrl- decreases the displayed font.

  3. Excellent display of data, and nice job explaining the details of the graph, which closely resembles a sine wave. A neat extension of this would be to superimpose a graph of the length of each day in Bend. There are some great advanced math concepts contained in here.

  4. Maybe you didn't change the size, but you changed the font, and it appears smaller. No problem, though -- I'll just get higher power trifocals.

  5. Well, I didn't change anything for posting, but I did change browsers, from FireFox to Google Chrome and that should not affect the fonts used in the posts, but I see that when I view the blog in FF it looks different than when I see it in Chrome. However, near as I can tell, this latest post looks pretty much the same as those from the past. I'll take a little more time later today to see if the underlying html is different.

  6. I'm viewing it with Firefox, so that might explain my problem. However, it looks more readable now. Thanks for your efforts.

  7. Hi Jack,

    Thanks so much for visiting my blog. In case of emergency, family members should immediately head to the Pilot Truck Stop. I really like your blog, and am now a follower.

    You and the Mrs. take care!


  8. I've been away from Bend for close to three weeks ... how nice to find this waiting for me!


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