How long is a day?

Posted in astronomy, math at 5:39 pm by danvk

As we approach the winter solstice, the days get shorter and shorter. There’s a common misconception about how quickly this change happens. Most people know that:

  1. The summer solstice (June 21) is the longest day of the year.
  2. The winter solstice (December 21) is the shortest day of the year.
  3. The days get shorter between Summer and Winter.
  4. The days get longer between Winter and Summer.

Many people take these four pieces of information and assume that the day length changes like this over the course of the year:

(The x-axis is the date. The y-axis is length of the day in hours.)

This is consistent with the four pieces of information, but is incorrect! There aren’t many sharp edges like that in Physics. Reality is much smoother:

The length of the day slowly increases as we approach the summer solstice, then slowly decreases as we leave it. This is great — it means that there are lots of long days in the summer. As we get to the autumnal equinox, the rate of change hits a maximum. The same thing happens around the winter solstice, only in reverse.

The summer solstice is the longest day of the year, but not by much! Here’s some day lengths for San Francisco:

Date Day Length Difference
Jun 18, 2009 14h 46m 45s + 09s
Jun 19, 2009 14h 46m 51s + 06s
Jun 20, 2009 14h 46m 54s + 02s
Jun 21, 2009 14h 46m 54s < 1s
Jun 22, 2009 14h 46m 50s − 03s
Jun 23, 2009 14h 46m 43s − 06s
Jun 24, 2009 14h 46m 33s − 10s

The lengths of the days around the solstice differ by only a few seconds! On the other hand, here are some day lengths around the autumnal equinox (September 22):

Date Day Length Difference
Sep 19, 2009 12h 15m 35s − 2m 24s
Sep 20, 2009 12h 13m 10s − 2m 24s
Sep 21, 2009 12h 10m 46s − 2m 24s
Sep 22, 2009 12h 08m 21s − 2m 24s
Sep 23, 2009 12h 05m 56s − 2m 24s
Sep 24, 2009 12h 03m 32s − 2m 24s
Sep 25, 2009 12h 01m 07s − 2m 24s

The length of each day changes by several minutes in September. Over a single week the day gets a whole 15 minutes shorter!

note: the interactive graphs are dygraphs, a JS library I created. Check it out!


Healdsburg Half Marathon

Posted in personal, sports at 1:25 pm by danvk

I ran my first half marathon this weekend, the Healdsburg Half in scenic California wine country. The race was held on Halloween, and no small number of runners came in costume. This is a nice twist on the usual “what should I be for Halloween” dilemma. Instead, it’s “what should I be that I can sweat in for 13 miles?”

My first goal was to finish. My second goal was to finish in under two hours. And I did! Final time was 1:54:33.1 (they are apparently very precise about these things!)

A race like this is a field day for data junkies like me, especially when you jog with an iPhone app like RunKeeper. I had it going for the first 10 miles, before my phone ran out of batteries. Here’s the track and mile splits:

mi pace
1 9:40
2 9:43
3 8:54
4 8:21
5 8:57
6 9:10
7 8:57
8 8:40
9 8:21
10 8:20

I must have picked it up after that — my pace over the remaining non-iPhone miles was 8:14/mile.

Some more stats and thoughts on what to do differently next time:

  • My co-worker Jeremy suggested that a good goal for a first half marathon would be a “reverse split”: running the second half faster than the first. I did that, too! The first 6.6 miles took 61 minutes, so the second must have taken 53. I guess I should have run the first half faster!
  • I should have charged my iPhone the previous night! More important than recording a track, it let me know exactly how far I’d gone: “6.34 miles” instead of “a few minutes past that six mile marker”.
  • I should have brought a jacket with me to the start. The race started before dawn and it was very cold! They even transported stuff to the end of the race for the runners. Something to remember for next time.
  • Running with a friend is great and can be good motivation. I ran most of the race with my friend Erica, who shaved a full 20 minutes off her previous half marathon time!
  • Erica’s dentist (a former marathoner) told her that she should take a drink at every water station. This was good advice. The only drink station I skipped was the one serving wine samples!

The Healdsburg Half was very well-organized. They had full results (PDF) posted the day of the race. I finished 396/1438 overall, 234/496 amongst men and 40/76 amongst 25-29 men.