When is the average sunrise?
When is the average sunset?
These are excellent questions to ask on the day the clocks go forward.
You might expect the average sunrise to be at 6am but this is not the case.
You might expect the average sunset to be at 6pm but this is not the case.
You might expect both to occur at the equinoxes but this is not the case.
n.b. For 'average' I'm using the arithmetical mean.
n.b. I'm using data for London in 2021.
n.b. In other places times may be earlier or later.
n.b. In other years dates might be a day or so out.
The simplest way to start is to pretend that we don't put the clocks forward.
A graph of sunset times would then be a simple sine curve.
Here's a sunset graph assuming Greenwich Mean Time all year round.
If you calculate the average sunset (by adding up all the times and dividing by 365)
you get 6.10pm. That's the red line on the graph.
n.b. The average sunset time is a bit later than 6pm because...
...the sun takes a finite time to set (about four minutes)
...the Earth's orbit isn't quite circular
...solarnoon isn't actual noon
n.b. The time of sunset varies from 3.52pm in December to 8.23pm in June.
Halfway between these is 6.07pm, which is pretty close to 6.10pm.
Sunset was at 6.10pm on 18th March, two days before the spring equinox.
Sunset would be at 6.10pm on 18th September, four days before the autumn equinox.
On the graph, note how sunset isn't close to the average for much of the year.
Sunset is within 1 hour of the average time for just 120 days a year.
This is because the graph is steepest in March and September.
If we didn't have British Summer Time I could end my post here.
But we do, and that hourly shift makes things rather more complicated.
Here's a sunset graph including British Summer Time.
The graph shoots up at the end of March (today!) from 6.25pm to 7.27pm.
The graph falls back at the end of October from 5.39pm to 4.37pm.
n.b. British Summer time lasts for seven months, or approximately 210 days.
This adds an extra hour for 210/365 of the year.
210/365 of an hour is about 35 minutes.
Hence the BST average is 35 minutes later than the GMT-only average.
If you calculate the average sunset you get 6.45pm.
That's the red line on the graph. 6.45pm is London's average sunset.
Interestingly there's only one day in the year with an average sunset.
Today's clock change leapfrogged past 6.45pm, so there isn't an average day in March. The only day with an average sunset is September 29th.
On the graph, note how sunset isn't close to the average for much of the year.
Sunset is within 1 hour of the average for only three months a year.
Sunset is more than 2 hours from the average for 5½ months a year!
That's 13 weeks before 4.45pm and 12 weeks after 8.45pm.
And sunset's the easy one.
Sunrise is nudged in the opposite direction.
Here's a sunrise graph including British Summer Time.
The graph reverses at the end of March (today!) from 5.48am to 6.46am.
The graph reverses again at the end of October from 7.51am to 6.53am.
This creates some rather different outcomes.
If you calculate the average sunrise you get 6.30am.
That's the red line on the graph. 6.30am is London's average sunrise.
Intriguingly there are three days in the year with an average sunrise.
One was three weeks ago (on my birthday).
Putting the clocks forward creates another in a week's time.
September has one but October doesn't because the clocks go back much later. The three days with an average sunrise are March 9th, April 4th and September 10th.
On the graph, note how sunrise is often quite close to the average.
Sunrise is within 1 hour of the average for six months a year.
Sunrise is never more than 2 hours from the average!
So... sunrise occurs within a range of 3½ hours (and has a standard deviation of 1 hour)
But... sunset occurs within a range of 5½ hours (and has a standard deviation of 2 hours)
And this is why, when we think of daylight saving, we think of evenings more than mornings.
Not only are we more likely to be awake,
but sunset times vary a lot more than sunrise times.
Hang on in there and sunset will eventually be two hours later than it is today.
But it's already 40 minutes better than average.
